Bring a large pot of salted water to a boil and cook rigatoni until al dente, reserving 0.5 cup of pasta water before draining.
In a large skillet or Dutch oven over medium-high heat, brown the ground beef and Italian sausage, breaking them into small crumbles until no pink remains.
Drain the excess fat from the skillet, leaving approximately 1 tablespoon in the pan for flavor.
Reduce heat to medium and add the butter and minced garlic to the meat, sautéing for 90 seconds until fragrant.
Pour in the heavy cream and bring to a low simmer, whisking constantly to incorporate the pan drippings.
Stir in the Parmesan cheese, oregano, red pepper flakes, salt, and pepper until the cheese is melted and the sauce has slightly thickened.
Add the cooked rigatoni to the skillet and toss to coat thoroughly, adding the reserved pasta water 1 tablespoon at a time if the sauce is too thick.
Spread the shredded mozzarella evenly over the top of the pasta and cover the skillet with a lid for 2 minutes until the cheese is fully melted and bubbly.
Garnish with chopped fresh parsley and serve immediately.