A broad professional background is important to operating in complex environments. How do you broaden your professional background?

I think you are a little ahead of yourself. Learn the Platoon and Company. Broadening starts there, on a firm technical tactical base to build on. The biggest thing you can do is have a good professional reading regime for your self. Have a variety. Perhaps identify a field grade that has similar interests to have deliberate conversations with about these books and topics over a beer or cup of coffee.

Go outside the box... Computing to Neuro-psychology to Artificial Inteligence to Data Mining... meanwhile, history, political science, statistics, chemistry ... the limit lies within you... go until you find it.

I look for ways to improve on skills I already have. For example, I blog. That led me to learn more about HTML/CSS/web design, social media management, graphic design, and effective communication.

I've done similar with music and open source software.

What do you do and recommend?

Well, for myself, I read just about anything that I can get my hands on, not just for my current field of work, but for things around me (as a Mechanic, I also learned welding, fuel handling, parts requests, recovery, all for wheels, got some lessons from 1/4 INF over the hill on tracks, and the 88) all these things are close to or can pertain to my job as a wheel mech. at the same time, I did my best to maintain my proficency as an 11B, studied all the mail classes I could get my hands on. If I saw something that tickled my fancy, or I could relate it to past, current or possible future jobs, I would read about it, or ask questions to clarify what is going on here or there. I may not have gotten degrees in many things, but when a question is asked, I either know the answer or I know who to get with to find the answer (which teaches me even more).
I would have to ask the question though. Broaden your Professional background... are you looking for paperwork for the resume to look pretty, or are you looking for actionable intel for your brain. By all means, grab any class you can for certs and sheepskins, but SOMETIMES, people are looking for that "more" of someone who can work in and out of their fields effectivly, or have enough knowledge to know when it is time for "hands off ask for help"

2LT (Join to see) Having a broad professional background is what I have enjoyed about the Army Reserve. I have been able to have a civilian career in software engineering and serve 31 years in both the National Guard and the Reserve. As have served as a 25A, 53, 88B, 90A in the military. I have had the benefit of developing and managing small groups and large teams of personnel in administrative and combat environments and have enjoyed the challenges of each.
The key is always look for the related next learning step advocated by the Army or your mentorship. If you don't have a mentor then book a meeting on your own initiative with your Sr. Rater and ask to be mentored.