Preheat your oven to 375°F (190°C).
In a large pot, bring salted water to a boil and cook the penne pasta according to package instructions until al dente. Drain and set aside.
In a large mixing bowl, combine the cooked pasta, shredded chicken, heavy cream, ¾ cup of Parmesan cheese, minced garlic, Italian seasoning, salt, and black pepper. Mix until well combined.
Transfer the pasta mixture to the baking dish and spread it evenly.
In a small bowl, mix the remaining ¼ cup of Parmesan cheese with the shredded mozzarella cheese. Sprinkle this mixture over the pasta bake.
Drizzle olive oil over the top of the cheese topping for added richness.
Cover the baking dish with aluminum foil and bake in the preheated oven for 20 minutes.
Remove the foil and bake for an additional 10 minutes, or until the cheese is bubbly and golden brown.
Once cooked, remove from the oven and let it sit for 5 minutes before serving.
Garnish with fresh parsley if desired.