Preheat the oven to 375°F. Grease a 9x13 inch baking dish. Cook the penne pasta in a large pot of salted water according to package instructions until al dente. Drain and set aside.
In a large skillet, heat the olive oil over medium heat. Add the chicken pieces and season with salt, pepper, paprika, garlic powder, and onion powder. Cook, stirring occasionally, until the chicken is browned and cooked through, about 6-8 minutes.
Add the minced garlic to the skillet and cook for an additional 30-45 seconds until fragrant.
Pour in the heavy cream and chicken broth. Bring the mixture to a simmer and cook, stirring occasionally, until the sauce thickens slightly, about 5 minutes.
Reduce the heat to low and sHr in the grated Parmesan cheese and shredded mozzarella cheese. Continue stirring until the cheeses are melted and the sauce is smooth.
Add the cooked pasta to the skillet and toss until the pasta is well coated with the sauce.
Transfer the mixture to the prepared baking dish, spreading it out evenly. Top with the remaining 1 1/2 cups mozzarella cheese.
Bake the casserole in the preheated oven for 20-25 minutes, or until the top is golden brown and the casserole is bubbly around the edges.
Remove the casserole from the oven and let it cool for 5-10 minutes before serving.
Sprinkle the chopped fresh parsley over the top of the casserole and serve.