Nice looking broomii you have. To answer your question, I must ask you a question. What do you want your aloe to do? If you desire growth above the ground, pot it in a 6" pot. Some feel if you stunt an aloe's root growth, you force the above soil growth. Also, you may force the aloe to offset or flower earlier. I am unaware if broomii offsets. If you want a solid root system, put it in an 8" pot. At that point, with all the growing room, it will put more of the energy into its' roots rather than into the leaves. In southern California, some aloes are voracious growers and will make the jump from a 3" pot to an 8" pot in one growing season. In Utah, they may not do that.
Personally, I prefer deep to shallow pots, although I do have a few exceptions. I hope this helps.

I would start by unpotting it, and looking at the roots. They may not be coming out of the drainage hole at the bottom, but could still be circling around the inside of the bottom. If so, I would move up one size (about a 4"), preferably deeper rather than shallow. If it likes its conditions, you may need to pot up again in a couple of months. I think that broomii can get to be about 2 to 3 feet across.