Toss chicken pieces with 1 tablespoon Cajun seasoning until evenly coated. Heat oil in a large skillet over medium-high heat. Add chicken in a single layer and cook undisturbed for 4 minutes until deeply browned. Flip and cook 3 minutes more until just cooked through. Transfer to a plate; do not wipe the skillet.

Bring a large pot of salted water to a boil. Cook penne 2 minutes less than package directions for al dente (it will finish in the oven). Reserve 1 cup pasta water, then drain and set aside.

In the same skillet used for chicken, melt butter over medium heat. Add onion and bell pepper; cook 5 minutes until softened and starting to brown at the edges. Add garlic and remaining 1 tablespoon Cajun seasoning; cook 1 minute until fragrant.

Sprinkle flour over vegetables and stir constantly for 2 minutes to cook out the raw taste. Gradually whisk in chicken broth, scraping up any browned bits from the pan. Bring to a simmer and cook 3 minutes until slightly thickened. Stir in heavy cream and hot sauce; simmer 2 minutes more. The sauce should coat the back of a spoon.

Stir cooked pasta and chicken into the sauce, adding reserved pasta water a splash at a time if needed to loosen. Taste and adjust seasoning. Transfer to a greased 9x13 inch baking dish, spreading evenly.

Preheat oven to 400F. Top with mozzarella and Parmesan. Bake uncovered for 20-25 minutes until bubbling at the edges and cheese is spotty golden brown. Let rest 10 minutes before serving. Garnish with parsley and pass extra hot sauce at the table.