In a medium bowl, toss the diced chicken with Cajun seasoning until well coated.
In a large pot of salted boiling water, cook the penne pasta according to package instructions until al dente. Drain and set aside.
In a large skillet, heat olive oil over medium heat. Add the seasoned chicken and cook until it’s golden brown and cooked through, about 7-8 minutes. Remove the chicken from the skillet and set it aside.
In the same skillet, add minced garlic and sauté for about 1 minute until fragrant.
Pour in the heavy cream and chicken broth, stirring to combine. Bring to a simmer and cook for 3-4 minutes until slightly thickened.
Stir in half of the Parmesan cheese and the shredded mozzarella cheese, mixing until smooth.
Add the cooked pasta, sautéed chicken, and chopped spinach to the cheese sauce. Stir gently to combine all ingredients, and season with salt and pepper to taste.
Transfer the mixture into a greased baking dish and top with the remaining Parmesan cheese.
Bake in the preheated oven for about 20-25 minutes, or until the top is golden and bubbly.
Remove from the oven, let cool for a few minutes, and garnish with fresh parsley if desired.