Heat oven to 375°F. Lightly grease a 9x13-inch baking dish.
Boil noodles in a large pot of salted water until flexible, just shy of al dente. Drain well.
Pat chicken dry. Season with 1 tablespoon Cajun seasoning, 1/2 teaspoon salt, and black pepper.
Heat olive oil in a large skillet over medium-high. Sear chicken until cooked through. Rest, then chop.
In the same skillet, sauté onion and peppers until softened. Stir in garlic for 30 seconds.
Add remaining 1/2 tablespoon Cajun seasoning, smoked paprika, and red pepper flakes. Cook 1 minute.
Melt butter in the pan. Sprinkle in flour and whisk for 1 minute to form a blond roux.
Slowly whisk in broth, then heavy cream. Simmer, stirring, until lightly thickened.
Whisk in cream cheese until smooth. Stir in 1 cup Parmesan. Season with remaining salt to taste.
Fold chopped chicken into the sauce and vegetables. Remove from heat.
Spread a thin layer of sauce in the dish. Add a layer of noodles.
Dollop half the ricotta over noodles. Spoon on one-third of the chicken sauce. Sprinkle mozzarella.
Repeat layers: noodles, remaining ricotta, another third of sauce, mozzarella.
Finish with noodles and the remaining sauce. Top with remaining mozzarella and 1/4 cup Parmesan.
Cover with foil, tented to prevent sticking. Bake 30 minutes.
Uncover and bake 12–15 minutes, until bubbling and lightly browned. Rest 15 minutes.
Garnish with parsley. Slice and serve warm.