In a large pot or dutch oven, heat olive oil over medium heat. Add the diced chicken breast, season with salt, pepper, and 1 tablespoon of Cajun seasoning. Cook until the chicken is browned and cooked through, about 7-8 minutes. Remove the chicken from the pot and set aside.
In the same pot, add the chopped onion and diced bell pepper. Sauté for about 3-4 minutes until the vegetables are softened.
Add the minced garlic and cook for another minute until fragrant.
Stir in the diced tomatoes (with juices), chicken broth, and the remaining Cajun seasoning. Bring to a boil.
Add the penne pasta to the boiling mixture. Reduce heat to a simmer and cover the pot. Cook for about 12-15 minutes, stirring occasionally, until the pasta is al dente and most of the liquid has been absorbed.
Stir in the cooked chicken, heavy cream, and mozzarella cheese. Continue to cook for an additional 2-3 minutes until the cheese has melted and the mixture is creamy.
Taste and adjust seasoning if necessary. Remove from heat.