Remove stems; remove brown gills from the undersides of mushrooms using a spoon.
Combine mushroom caps and next 5 ingredients (mushrooms through pepper) in a large zip-top plastic bag; seal. Marinate 30 minutes; remove mushrooms from bag, reserving marinade.
Preheat oven to 425°.
Place mushrooms and wine in a shallow baking dish. Bake at 425° for 10 minutes or until mushrooms are soft.
Place zucchini, yellow squash, and onion on a baking sheet; brush with reserved marinade. Bake at 425° for 10 minutes or until slightly soft.
Place 2 mushrooms, gill sides up, on a baking sheet; divide baked vegetables evenly between each mushroom. Top each with a tomato slice, 2 tablespoons cheese, and a mushroom. Bake at 425° for 10 minutes or until thoroughly heated.