Preheat the oven to 400°F (200°C). Grease the inside of a 12-inch ovenproof skillet with the 2 tablespoons softened butter; set the skillet aside.

In a medium bowl, stir together 2 cups self-rising flour and 1 1/2 cups heavy cream until just combined into a sticky dough. Do not overmix.

Press the dough into the bottom of the prepared skillet and up the sides about 2 inches to form a crust. Set the crust aside.

In a separate skillet over medium heat, crumble and brown 1 pound breakfast sausage, stirring and breaking it up until no pink remains, about 5 minutes.

Using a slotted spoon, transfer the browned sausage to a paper towel-lined plate to remove excess fat, then spread the drained sausage evenly over the dough in the skillet.

Sprinkle 1 1/2 cups grated Cheddar cheese evenly over the sausage.

In a bowl, whisk together 5 large eggs, 1/4 cup milk, 1/2 teaspoon kosher salt, and 1/4 teaspoon ground black pepper until blended.

Pour the egg mixture evenly over the cheese and sausage in the skillet.

Bake the quiche in the preheated oven until the eggs are set and the top is golden brown, about 20 minutes. Remove from the oven and let rest 5–10 minutes before slicing and serving.