1. Stem white mushrooms, and set caps upside down on baking sheet. Set aside. Chop stems, and add to chopped oyster mushrooms. (You should have about 2 cups total.)
2. Heat oil in medium skillet over medium heat. Add onion, and sauté 2 to 3 minutes, or until translucent. Add chopped mushrooms, and cook 15 to 20 minutes, or until browned. Stir in garlic and thyme; add rice, and cook 2 to 3 minutes, or until rice turns opaque. Add wine; simmer 2 minutes, or until most liquid has evaporated. Add broth, season with salt, and bring to a boil. Cover, reduce heat to medium-low, and simmer 18 to 20 minutes, or until most liquid is absorbed. Remove from heat, and stir in parsley. Cool.
3. Preheat oven to 400°F. Fill each mushroom cap with 1 heaping Tbs. rice mixture. (A small cookie scoop works well.) Bake 20 minutes, or until mushrooms are tender and rice begins to crisp on top.