Preheat oven to 350°.
Remove stem and brown gills from undersides of mushrooms using a spoon; discard gills. Place mushrooms, stem side down, on a baking sheet coated with cooking spray. Bake at 350° for 10 minutes; cool mushrooms on wire rack.
Heat oil in a large nonstick skillet over medium-high heat. Add onion; sauté 12 minutes. Stir in wine, vinegar, 1 teaspoon thyme, and salt; bring to a boil. Cover, reduce heat, and simmer 25 minutes. Uncover and increase heat to medium-high; cook 5 minutes or until liquid evaporates. Stir in olives, rind, and pepper.
Place bread in a food processor; pulse 10 times or until coarse crumbs measure 1 1/2 cups. Combine 1 teaspoon thyme, crumbs, cheese, and parsley. Spoon 1/2 cup olive mixture into each mushroom; top with about 3/4 cup cheese mixture. Bake at 350° for 25 minutes or until golden brown.