Preheat your oven to 350°F (175°C) and grease a 9x13-inch baking dish with the 1 tablespoon of unsalted butter.
In a large skillet over medium-high heat, cook 1 pound of bulk breakfast sausage, breaking it up with a spoon until it is browned and no longer pink, which should take about 8-10 minutes. Use a slotted spoon to transfer the cooked sausage to a paper towel-lined plate to drain, leaving about 1 tablespoon of drippings in the skillet.
Add the finely diced yellow onion and red bell pepper to the skillet with the drippings. Sauté over medium heat for about 5-7 minutes, stirring occasionally, until the vegetables have softened.
In a large mixing bowl, whisk together the 8 large eggs, 2 cups of whole milk, 1 teaspoon of kosher salt, ½ teaspoon of black pepper, and 1 teaspoon of dry mustard powder until the mixture is completely smooth and uniform.
Spread the 6 cups of cubed bread evenly in the bottom of the prepared baking dish. Top with the cooked sausage and sautéed vegetable mixture. Sprinkle 1 ½ cups of the shredded cheddar cheese over the top.
Slowly and evenly pour the egg mixture over the contents in the baking dish, ensuring all the bread is moistened. Gently press down on the top with a spatula to help the bread absorb the liquid. Let the dish stand for 10 minutes so the bread can soak up the custard.
Sprinkle the remaining ½ cup of shredded cheddar cheese over the top. Bake in the preheated oven for 45-55 minutes, or until the casserole is puffed, the center is fully set (doesn't jiggle when shaken), and the top is a deep golden brown.
Remove the casserole from the oven and let it rest on a wire rack for 10 minutes before slicing and serving. This allows the layers to set for clean cuts.