In a large pot, bring salted water to a boil. Add the penne pasta and cook for about 8-10 minutes until al dente. Drain and set aside.
In a large skillet, heat the olive oil over medium heat. Add the chicken pieces and sprinkle with Cajun seasoning. Cook for about 5-7 minutes until the chicken is browned and cooked through.
Add the minced garlic and chopped bell peppers to the skillet. Sauté for an additional 2-3 minutes until the bell peppers are slightly tender.
Reduce heat to low, then stir in the heavy cream and chicken broth. Bring to a gentle simmer, and then mix in the grated Parmesan cheese until melted and well combined. Add black pepper and salt to taste.
In a large mixing bowl, combine the cooked penne with the chicken Alfredo sauce. Mix well until the pasta is evenly coated.
Transfer the mixture into a greased 9x13 inch baking dish. Sprinkle shredded mozzarella cheese evenly over the top.
Bake in the preheated oven for 20-25 minutes, or until the cheese is bubbly and golden.
Remove from the oven and let it cool for a few minutes. Garnish with fresh parsley before serving.