Cook fettuccine until al dente. Reserve ⅔ cup pasta water before draining.
Pat chicken dry and toss with 1½ tbsp Cajun seasoning, smoked paprika, salt, and black pepper.
Heat olive oil and 2 tbsp butter in a large pan. Sear chicken 4 minutes without moving, flip and cook 3 minutes more until golden with crispy edges. Add 3 cloves garlic at the end. Remove and set aside.
Melt 3 tbsp butter in the same pan. Add onion and cook 4 minutes, then add 5 cloves garlic and cook 1 minute.
Whisk in flour and cook 2 minutes.
Pour in chicken broth while whisking, then add heavy cream and milk. Simmer 5 minutes until thickened.
Lower heat and stir in cream cheese until fully melted.
Add mozzarella, cheddar, and Parmesan in handfuls, stirring until heavy and glossy.
Season with the remaining 1 tbsp Cajun seasoning, garlic powder, onion powder, cayenne, and red pepper flakes.
Stir in the remaining 3 tbsp butter and last 2 cloves garlic, then add pasta water to loosen slightly.
Toss the fettuccine until every ribbon is tangled and buried in sauce.
Serve with the Cajun chicken arranged beside the pasta. Garnish with parsley and extra Parmesan.