Preheat oven to 375 degrees F. Bring water to a boil and prepare pasta according to directions. Cut chicken into 1-inch cubes and season with salt, pepper, paprika and basil.
Heat a large skillet over medium heat and add olive oil. Stir in onions and peppers with a pinch of salt, cooking for 5 minutes until soft. Add in garlic and stir. Increase heat to medium-high and add chicken in a single layer. Cook for 5-6 minutes until browned, then flip and cook for 5-6 minutes more. Stir in diced tomatoes, cream and parmesan cheese, mixing well to combine. Stir in penne.
Transfer mixture to a baking dish and top with mozzarella. Bake for 10-15 minutes, just until cheese is melted and pasta is warmed through. Serve immediately with extra cheese for grating.