Bring a large pot of salted water to a boil. Cook rigatoni according to package instructions until al dente. Reserve 1/2 cup of pasta water, then drain the pasta.
While the pasta cooks, season the chicken cubes with salt, pepper, garlic powder, and dried oregano.
In a large skillet over medium-high heat, melt 2 tablespoons of butter with the olive oil. Add the chicken bites in a single layer.
Sear the chicken for 5-7 minutes, turning occasionally, until golden brown and cooked through. Add the minced garlic during the last 60 seconds of cooking to prevent burning.
Remove the chicken from the skillet and set aside on a plate.
Reduce heat to medium. In the same skillet, add the remaining 2 tablespoons of butter and the heavy cream. Bring to a gentle simmer, scraping up any browned bits from the bottom of the pan.
Gradually whisk in the grated Parmesan cheese until the sauce is smooth and thickened.
Add the cooked rigatoni and chicken bites back into the skillet. Toss thoroughly to coat, adding reserved pasta water 1 tablespoon at a time if the sauce needs thinning.
Top the entire dish with shredded mozzarella cheese. Cover the skillet with a lid for 2 minutes or place under a preheated broiler for 1-2 minutes until the cheese is melted and bubbly.
Garnish with chopped parsley and serve immediately.