Brown the sausage in a large skillet over medium heat, breaking it into small crumbles as it cooks (8-10 minutes) until no pink remains. Drain excess fat on paper towels.
In a large bowl, whisk together eggs, milk, dry mustard, salt, pepper, and optional nutmeg until well combined and slightly frothy.
Grease a 9x13-inch baking dish with butter. Layer the bread cubes evenly across the bottom, followed by the cooked sausage, diced red peppers and green onions. Sprinkle with most of the cheese, reserving about 1/4 cup for topping later.
Pour the egg mixture slowly and evenly over the assembled ingredients. Gently press down with a spatula to ensure all bread pieces are moistened. Cover tightly with plastic wrap and refrigerate overnight (or at least 8 hours).
When ready to bake, remove the casserole from the refrigerator and let it stand at room temperature for 30 minutes. Preheat your oven to 350°F (175°C).
Sprinkle the reserved cheese on top and bake uncovered for 45-50 minutes until puffed, golden brown, and set in the center. A knife inserted in the center should come out clean.
Let rest for 10-15 minutes before cutting into portions and serving.