Cook sausage in a large skillet over medium-high until browned and crumbly; remove and drain on paper towels.
Sauté peppers, onion, and mushrooms in same skillet about 5-7 minutes until softened; set aside to cool.
Whisk eggs, milk, salt, pepper, and paprika in a large bowl until thoroughly combined.
Grease a 9x13-inch dish; layer half the bread, sausage, bacon, vegetables, both cheeses, then remaining bread.
Pour egg mixture evenly over casserole; press to soak bread. Cover tightly with foil; refrigerate overnight.
Preheat oven to 350°F. Bake covered 40 minutes; uncover and bake another 15 minutes until top is golden and center set. Garnish with green onions before serving.