Boil the spaghetti. Cook the spaghetti in salted water until just al dente, then drain and set aside.
Coat the chicken. Pat the strips dry, season with 1 teaspoon Cajun seasoning, the paprika, salt, and pepper, then press into the 1/2 cup Parmesan.
Cook the chicken. Heat the oil in a large deep skillet over medium high heat and cook the strips 5 to 7 minutes until golden and 165 degrees F inside. Stir in 2 tablespoons butter and half the garlic for the last minute, then move to a plate.
Start the sauce. Melt the remaining butter in the pan, cook the remaining garlic 1 minute, then add the cream and broth and simmer on low.
Melt the cheeses. Stir in the cream cheese, mozzarella, cheddar, and 3/4 cup Parmesan until smooth. Add the Italian seasoning, basil, remaining Cajun seasoning, and pepper flakes. Simmer 5 minutes until thick.
Combine. Toss the spaghetti in the sauce, top with the chicken, and garnish with parsley.