What are good examples of broadening assignments to advise to your troops, to further their careers?

Defense Attaché Service. It is a joint environment where you serve in U.S. Embassy's around the world.

The Army Attaché Management Division represents the U.S. Army in selecting highly-qualified Regular Army personnel for assignment within the Defense Attaché System. Army Attaché personnel serve around the world in United States Embassies within a Defense Attaché Office (DAO). The DAO represents the Department of Defense to the host-nation government and military, assists and advises the U.S. Ambassador on military matters, and coordinates.

Consider assignments that can provide multiple, simultaneous benefits. For instance, professionally, serving at a Combat Training Center (JRTC/NTC/CMTC) is a great professional experience for both officers and NCOs, but they are not excessively demanding on time as one would find with being a Drill Sergeant or Ranger Instructor. This extra time would allow the leader to purse education -- maybe finish a Bachelor's Degree or earn a Masters Degree. If they are efficient and are good at time management, they will also have time for persona (family) pursuits, something that is never bad when we are away from the tactical Army.

Another path would be to serve above the tactical level -- pursue a job at a Service Component Command (5th Army, 3rd Army, USAPAC etc) in order to see how other levels of defense and the government work. Many of these headquarters (or if the jobs are available, combatant commands) are in locales where many in the tactical disciplines will never be assigned, and there is a learning and exposure that will definitely broaden the professional soldier.

Compare what is available -- ROTC, Recruiting also may offer the opportunities to purse secondary pursuits as well, while being a Drill Instructor remains one of the best paths for promotion in DA selected boards, especially for combat arms -- and choose the opportunity that offers the most "bang for the buck". But take advantage of the opportunity of the only thing that is "broadened" are your skills at procrastination and being lazy!