Melt 5 tablespoons butter in a large skillet over medium-high heat. Saute bacon crumbles and onion in hot butter until onion is tender, 5 to 10 minutes. Add eggs; cook and stir until eggs are starting to set but are still moist, about 5 minutes.
Melt 5 tablespoons butter in a saucepan over medium-high heat. Whisk flour into butter to form a thick paste. Add milk, Cheddar cheese, salt, and pepper. Cook and stir until cheese is melted and sauce is thick, 5 to 7 minutes.
Stir seasoned stuffing mix and 1/4 cup melted butter together in a bowl.
Grease a 9x13-inch baking dish.
Stir eggs and cheese sauce together in a bowl; pour into prepared baking dish and spread stuffing mixture over the top. Cover the baking dish with plastic wrap and chill in the refrigerator, 8 hours to overnight.
Preheat oven to 350 degrees F (175 degrees C). Remove plastic wrap from baking dish.
Bake casserole in the preheated oven until heated through and set, about 30 minutes.