Place chicken breast between 2 pieces of plastic wrap and with the flat side of a meat mallet, pound to 1/4-inch thickness. Season with salt and pepper to taste.
In a skillet over medium heat, add bacon. Cook until it begins to render fat and crisps. With a slotted spoon, remove from pan and drain on paper towels.
Discard bacon fat except for about 1 tablespoon. Add onions and saute until limp.
Add mushrooms and cook, stirring occasionally, until softened. Remove from pan and allow to cool completely.
On one end of the chicken breast, spoon 1/4 of the bacon-mushroom mixture and 1/4 of the cheese.
Wrap chicken breast over filling and roll into a tight log. Secure with toothpicks, if necessary. Repeat with remaining chicken.
In a wide, shallow dish, combine bread crumbs, Italian seasoning, and garlic powder. Carefully dredge rolled-up chicken in bread crumbs until fully coated.
Place stuffed chicken in a single layer, seam side down, on a lightly-greased baking sheet.
Drizzle with melted butter or spray with nonstick cooking spray.
Bake in a 425 F oven for about 20 to 25 minutes or until golden brown on the outside and thermometer inserted in the center reads 165 F.
Remove from oven and allow to stand for about 1 to 2 minutes before slicing. Serve hot.