Preheat oven to 350 degrees F (175 degrees C).
Heat a large skillet over medium-high heat. Cook sausage, breaking it apart with a wooden spoon, until browned and crumbly, 5 to 7 minutes. Spread over the bottom of a 9×13-inch casserole dish.
Mix eggs, Cheddar cheese, cream, onion, mustard, oregano, salt, and pepper together in a bowl. Pour mixture over the sausage.
Bake in the preheated oven until firm and cooked through, 30 to 40 minutes.
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