Preheat the oven to 375 degrees Fahrenheit (190 degrees Celsius) and grease a 9x13 inch ceramic baking dish with butter.
Place a large skillet over medium-high heat and cook the ground sausage until fully browned and crumbled, approximately 8-10 minutes. Drain the rendered fat.
In a large mixing bowl, whisk the eggs, whole milk, salt, black pepper, and dry mustard powder until the mixture is homogeneous.
Distribute the cubed bread evenly across the bottom of the prepared baking dish to form a base layer.
Layer the browned sausage evenly over the bread cubes, followed by the shredded cheddar cheese.
Pour the egg and milk mixture slowly over the layers, ensuring all bread cubes are saturated.
Transfer the dish to the center rack of the oven and bake for 40 to 45 minutes, or until the custard is set and the internal temperature reaches 160 degrees Fahrenheit.
Remove from the oven and allow the casserole to rest for 10 minutes to stabilize the structure. Garnish with chopped chives before slicing into 8 portions.