Sweating something is a way of cooking it so that it gets hot (and releases a little liquid) but doesn't turn brown. So, you get a cooked vegetable without having it brown. At long last, in spite of my earlier troubles, I've achived this with fresh garlic at a high heat with bok choy.
The trick was not thicker garlic. I thought about it a bit and realized how dumb I was being. The problem was that I was burning the outside of the garlic, not that I was cooking the middle of it too quickly. So, I threw the minced garlic into the oiled pan, pulled the pan off the heat, tossed the garlic a bit and let them sweat and cool for a few seconds, set the pan down off the heat, threw in my bok choy stems, and returned the pan to the heat. Then I tossed the pan a bit more before I threw in the "chicken stock powder" (I used some indeterminate amount of Better Than Boullion because I forgot and panicked at the last second) and the leaves. Returned it to the heat, tossed a bit more until it was cooked, and set it off the heat to season with soy and seseame oil.
Voila! Wonderful garlic flavor on my stir-fried bok choy!