Clean mushrooms well. Remove stems and carve out a portion of the center of each mushroom. Finely chop stems and carvings and set aside.
In a large skillet, sauté mushroom caps for 2 to 4 minutes in 2 tablespoons of the butter or oil. Remove caps and place hollow-side up on a greased baking sheet.
In the same skillet, brown onions on high heat for a few minutes, stirring constantly. Add remaining butter or oil. Sauté onions over medium-low heat for 5 minutes.
Add chopped mushrooms and seasonings to the skillet. Cook 5 more minutes. Stir in bread crumbs and cheese.
Fill caps with stuffing. Place under preheated broiler for 5 minutes or until nicely browned.