Preheat oven to 400°F. Remove sausage from casing and place in a medium skillet. Cook meat over medium heat, breaking it up with a wooden spoon and stirring occasionally, until crumbly and browned, about 7 minutes. Transfer sausage to a bowl.
Melt butter in same skillet over medium heat. Add mushroom stems, onion and garlic and cook, stirring, until softened, about 4 minutes. Remove from heat and add bread, cheese, parsley, oregano and reserved sausage. Stir well to mix.
Stuff sausage mixture firmly into mushroom caps. Place caps on a foil-lined baking sheet. Bake until tops are crusty and mushrooms are tender, 10 to 15 minutes.