Preheat your oven to 375°F (190°C). Bring a large pot of salted water to a boil and cook the penne pasta according to package instructions until al dente. Drain and set aside.
Heat the olive oil in a large skillet over medium heat. Add the sliced chicken andouille sausage and cook for about 5 minutes until browned. Remove the sausage and set aside. In the same skillet, add the diced onion, green bell pepper, and garlic. Sauté until softened and fragrant, about 4 minutes.
Return the sausage to the skillet. Stir in the undrained diced tomatoes, chicken broth, heavy cream, Cajun seasoning, dried oregano, salt, and black pepper. Simmer the sauce for 8–10 minutes, allowing the flavors to meld and the sauce to thicken slightly.
Add the cooked penne pasta to the skillet and stir until every piece is coated with the creamy, spicy sauce.
Transfer the pasta mixture to a greased 9x13 inch baking dish. Sprinkle the shredded mozzarella and grated Parmesan evenly over the top. Bake uncovered for 20–25 minutes, or until the cheese is melted and bubbly with golden spots.
Remove from the oven and let it cool slightly. Sprinkle chopped fresh parsley over the top for a pop of color and freshness before serving.