Preheat the oven to 350 degrees. Spray a 9x12-inch baking dish with cooking spray.
Remove the sausage from the casings and crumble into a large skillet. Add the onion and cook over medium heat until the sausage is no longer pink and the onions are translucent, about 8 minutes. Drain.
Whisk together the eggs, milk, mustard, salt, and pepper. Add the sausage, hash browns, and 1/2 the grated cheese. Pour into the prepared baking dish. Top with the remaining cheese and the diced peppers. Bake, uncovered, for 45-55 minutes or until the center is just set. Let cool 10 minutes before serving.