Butter a 9x13 inch dish; set aside.
Whisk eggs, milk, salt, and pepper in a large bowl until combined.
Stir in bread, cheese, peppers, broccoli, onion, and garlic to coat evenly.
Pour into dish; drizzle with melted butter. Cover tightly with plastic wrap; refrigerate overnight.
Next morning, remove from refrigerator; stand at room temperature 20 minutes while preheating oven to 350°F.
Remove plastic wrap; bake uncovered 45 minutes until golden brown and center set.
Cool 5 minutes before slicing and serving.