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Preheat the oven to 350 degrees F (180 degrees C). Butter a 9x13-inch baking dish.
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Heat a large skillet over medium-high heat. Cook and stir sausage in the hot skillet until browned and crumbly, 5 to 7 minutes. Drain and discard grease. Set aside to cool slightly.
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Add butter to a griddle over medium-high heat; spread potatoes in an even layer, and cook until golden, 5 to 6 minutes per side. Add potatoes to the bottom of the prepared baking dish.
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Whisk eggs and cream together in a large bowl. Whisk in dry mustard and season with salt and pepper. Stir sausage and 8 ounces Cheddar cheese into eggs. Pour mixture over potatoes, and smooth out the top. Cover the dish tightly with foil or an oven-safe lid.
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Bake in the preheated oven until eggs are nearly set, 30 to 40 minutes. Remove from the oven, remove foil, and scatter remaining cheese over the top.
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Return casserole to the oven and bake until eggs are no longer jiggly, about 10 minutes. Turn the oven up to Broil, and broil until top is browned and crispy, a few minutes more.
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Serve immediately with hot sauce.