Wash mushrooms and remove stems from the mushroom caps. Finely chop the stems into small pieces.
In a skillet over medium heat melt the butter. Add in the finely chopped mushroom stems, and onions, and minced garlic. Add in salt, pepper, and thyme. Cook until onion is softened.
Add breadcrumbs and stir well to combine into a stuffing. Using a small spoon, stuff the mushrooms firmly with the stuffing mixture. You may have a little left over.
Place the stuffed mushrooms in a baking dish, place some finely grated Swiss cheese on the top of the mushrooms, and bake at 350 for about 20 min. Serve hot.