Preheat oven to 350°F (175°C) and grease a 9x13-inch baking dish.
In a large skillet, brown the ground sausage over medium heat until fully cooked. Drain excess fat and set aside.
In a medium bowl, whisk together the eggs, milk, dry mustard, salt, and black pepper until well combined.
Distribute the bread cubes evenly in the bottom of the prepared baking dish.
Layer the cooked sausage over the bread cubes, followed by an even layer of shredded cheddar cheese.
Pour the egg and milk mixture evenly over the sausage and cheese layers.
Bake for 40 to 45 minutes, or until the eggs are set and the top is golden brown.
Allow the casserole to rest for 5 to 10 minutes before slicing and serving.