In a large skillet over medium-high heat, brown the sausage and onion together, stirring until the meat is no longer pink (about 7 minutes). Drain the excess grease and set aside.
Grease a 13 x 9-inch baking dish. Spread the cubed bread evenly in the bottom of the dish. Layer the cooked sausage and onion mixture on top, followed by the grated cheddar cheese.
In a large bowl, whisk together the eggs, milk, dry mustard, kosher salt, and black pepper until well combined.
Pour the egg mixture over the casserole, making sure it soaks into the bread. Press down gently with a spatula to help the bread absorb the liquid.
Cover the dish tightly with foil and refrigerate for 8 hours or overnight.
The next morning, remove the casserole from the fridge and let it rest on the counter for 30-60 minutes to come to room temperature. Preheat your oven to 350°F (175°C).
After resting, remove the foil and bake the casserole (uncovered) for 60-80 minutes, or until the eggs are set and a knife inserted into the center comes out clean. If it begins to brown too quickly, cover loosely with foil.
Let the casserole sit for about 10 minutes before slicing it into squares. Serve warm.