Preheat your oven to 375°F (190°C) to ensure even baking.
Gently clean the cremini mushrooms with a damp paper towel and remove the stems to create hollow spaces for the filling. Finely chop the stems and set aside.
In a skillet, melt the butter over medium heat. Add the minced onion and sauté until translucent, about 3-4 minutes. Stir in the garlic and chopped mushroom stems, cooking for another 2-3 minutes.
In a mixing bowl, combine the sautéed mixture with mozzarella, 1/2 cup of Parmesan, breadcrumbs, and thyme. Mix until creamy and well combined.
Fill each mushroom cap with the cheesy mixture, packing it slightly.
Place the stuffed mushrooms on a baking sheet. Drizzle with olive oil and sprinkle with remaining Parmesan. Bake for 20-25 minutes until golden brown.
Remove from oven, let cool slightly, garnish with thyme, and serve warm.