Preheat oven to 350°F (175°C).

Grease a 9 x 9-inch baking dish.

Brown sausage in a skillet over medium heat.

Drain excess grease and let the sausage cool slightly.

In a large bowl, beat eggs and milk together until well combined.

Add the cooled sausage to the egg and milk mixture.

Remove crusts from bread slices and cut the bread into cubes.

Add the cubed bread, salt, dry mustard, and cubed Cheddar cheese to the sausage mixture.

Stir all ingredients together until evenly distributed.

Pour the mixture into the prepared baking dish.

Bake in the preheated oven for 45 minutes, or until golden brown and set.