Preheat the oven to 350°F (175°C).

Cook chopped bacon and sausage in a large skillet over medium-high heat until browned and crispy, about 600 seconds. Drain on paper towels.

Brush butter on the bottom and sides of a 9x13-inch baking dish, then sprinkle grated Parmesan cheese over the bottom. Layer the bacon and sausage on top.

Spread shredded Cheddar cheese evenly over the meat mixture.

Beat eggs, heavy cream, and half-and-half in a large bowl. Slowly pour this mixture over the cheese and meat.

Bake in the preheated oven until the quiche sets and a knife inserted in the center comes out clean, approximately 3600 seconds.