This is adapted from a recipe on drfuhrman.com. I made some changes to better fit our taste preferences and simplified the instructions. You can reduce prep time by using frozen chopped broccoli and jarred garlic.
Place vinegar in a small pan and boil over medium heat until it is syrup-like and reduced by half, about 3 minutes. Pour vinegar into a large bowl and whisk in mustard and thyme and set sauce aside.
Prepare garlic, broccoli, pepper and mushrooms.
Coat large covered non-stick frying pan or Dutch oven (at least 5 quarts) with oil. Add garlic, broccoli, pepper and mushrooms. Cook over medium heat, stirring frequently, adding small amount of water as needed to prevent sticking until broccoli is tender crisp.