Preheat oven to broil with rack 10 inches from heat source. Heat oil in a large nonstick skillet over medium-high. Add mushrooms in an even layer and cook, undisturbed, until bottoms are browned, about 4 minutes. Stir, then continue cooking, stirring occasionally, until browned all over, about 6 minutes. Remove from heat, and stir in honey and balsamic vinegar.