What do you do when a soldier refuses to listen to your directions?

In the new volunteer Army if the 70's ... insure the soldier does not have a profile allowing/requiring him to wear the eyewear. Give him one additional chance to remove the eyewear. Even if the soldier complies with the second order, insure he knows he has already violated a lawful order. If the soldier then complies, continue with your duty. At the next available time, inform the soldier he will be performing corrective training for his refusal to obey a order. Write up the incident for your Platoon Leader and First Sergeant. Under no circumstance do you get into a physical contest in front of the other troops.

If there is a second refusal, remove the eyewear as you are lawfully allowed to do. If there is physical resistance, dismiss the soldier from formation and order him to report to the orderly room and wait for your arrival. Detail another NCO to instruct the company clerk as to why the soldier is waiting. At the next available time ask two other senior NCO's to advise/assist/witness your well thought out completion of the situation ... confiscation of the eyewear, administration of corrective training (private physical correction may be available); write it up (to document for future events and to CYA) reporting the incident to your Platoon Leader and First Sergeant who may may choose administrative, UCMJ, punishment.

Go home an dream of pounding private dumbass into the dirt!

First things first, yes I am a SPC. Nevertheless while on active duty I had soldiers assigned to me and had counseling authority over them. With that in mind consider what I'm writing, not the rank I hold.
I do have one important question that I haven't seen addressed in the comments before I continue:
Why are you referencing the Army Command Policy on EO (AR 600-20) for information on counseling and UCMJ exactly? Information specific to the counseling process can be found in ATP 6-22.1 while information specific to the Uniform Code of Military Justice can be found within the UCMJ itself, with articles 77-134 describing offenses subject to punitive actions.
If you recommend a soldier for UCMJ over something like this, especially if there's no documented patter of disobedience reflected in their monthly developmental counseling statements the only outcome is going to be a really negative bullet on your next NCOER. Unless both your CO and 1st SGT are really old-school.
Write up an event-oriented counseling statement to reflect the soldier's refusal to obey your order. As a POA offer up something simple that allows the soldier an out, like a written essay/apology that will stay between you and the soldier.
EX: "PVT Snuffy, on 01 May 2016 you were instructed by myself (SGT Hamilton) to remove your sunglasses during a formation. This instruction was given because the sunglasses were unauthorized for wear per AR 670-1 for the following reasons (possessed a logo, etc.) You chose to ignore my instructions. As a result you are being counseled for your disobedience of a direct order in accordance with the UCMJ. Further incidents of this sort may result in recommendation for disciplinary action for violation of the UCMJ, specifically Article 91: Insubordinate Conduct toward Warrant Officer, Non-commissioned Officer or Petty Officer. As this is your first offense of this nature I am instead offering you corrective counseling to address your offense."
Your plan of action (POA) for the offending soldier would then read something like this:
EX: "Using the UCMJ (specifically Article 91,) AR 670-1 and FM-3-21.5 you will draft a 1000 word essay describing both how and why your actions on the morning of 01 May 2016 were wrong. This essay willl be constructed in accordance with the Chicago Manual of Style, copies of which are available at your local (or post) library and will contain relevant citations and quotations which are not to be counted toward the final total of 1000 words. This essay is to be submitted to myself (SGT Hamilton) no later than 0800 08 May 2016 for review."
If you think your soldier is an otherwise good soldier who just temporarily lost their mind you can take the issue more public without risking losing authority and write up a POA something like:
EX: "Following final formation on 01 May 2016 you will be offered the opportunity to address the formation. In doing so you will issue a public apology for your actions for the benefit of your fellow junior enlisted soldier's professional development in the form of an After Action Review detailing your refusal to follow my instructions, why that refusal was wrong and your own acknowledgement of this fact."
Following the event oriented counseling you need to make sure that the incident is addressed as a bullet in the soldier's monthly developmental counseling as well as whether or not they successfully completed the proscribed POA to correct their behavior... this is the "New Army" your counseling game needs to be on point after all!

write him up. start the paper work to boot him from the Service. Don't hit him don't yell and call him names. tell him he is excused from formation and to report to the Lt or CO.

As a former NCO, I would recommend him/her for UCMJ and as a former Company CDR I'd support you. Seems rather simple to me.

I am truly amazed at most of the SSG's responses. "Be touchy feely and find out what is bothering him then we'll all have a group hug". Dear God! What have the libtards done to the Army. Refusing a lawful order? Stomp a mud hole in his ass and kick it dry. Yeah its brutal but it works. The Army is not a democracy. Its totalitarian and I'm the Chief Dictator.

NJP. Enough said.

They'd fall off from all those miles, pushups and whatever the else I would do. Extreme example of this shit bird

I find it hard to believe that people are not sure why this incident happened.
1. Today's NCO's are a product of crappy leadership. There was a time when a E-3, E-4 didn't want any part of a NCO. We were masters of our universe and students of out craft. Now we have alot of people that stand on what they did over there and never had the chance to learn or understand doctrine or indoctrination. This is true on the officer and enlisted ends of the spectrum. Be butthurt all you want. Out leadership training is lacking. We have not learned from our past. Our NCO's do not understand the influence they has and because of this do not exercise it. Too many officer do not understand the NCO role. Out family is about as dyslexic as a brother and sister swinging group from West-by-god.

as far as ntc no cell phones, saw it many times sm's relieved of thier cell phones, i dont believe in the destruction of anothers personal property to satisfy authority, i do believe in njp, tank traps are a bitch, especially with an e tool, fox holes are another good training method, look to the past and adapt

First the assumption is that the punishment needs to occur immediately. No it doesnt. Failure to obey a direct order from an NCO in authority over you is a UCMJ violation. You call up the Legal office and you follow their instructions. After that I'm sure there wont be any further incidents.