01 - Bring a large pot of salted water to a rolling boil.
02 - Pat chicken breasts dry with paper towels. Sprinkle Cajun seasoning evenly over both sides, pressing gently to adhere.
03 - Heat olive oil in a large skillet over medium-high heat. Add chicken and cook for 5 to 6 minutes per side until blackened and cooked through, reaching an internal temperature of 165°F. Remove from pan and let rest for 5 minutes before slicing thinly.
04 - Add fettuccine to boiling water and cook according to package directions until al dente. Drain, reserving 1/2 cup of pasta water, and set aside.
05 - In the same skillet used for chicken, reduce heat to medium. Add butter and minced garlic; sauté for 1 minute until fragrant but not browned.
06 - Pour in heavy cream and whole milk. Bring to a gentle simmer, stirring frequently to prevent scorching.
07 - Stir in freshly grated Parmesan cheese until completely melted and sauce thickens slightly, about 2 to 3 minutes. Season with salt, black pepper, and cayenne to taste.
08 - Add cooked fettuccine to the sauce, tossing to coat evenly. If sauce is too thick, add reserved pasta water a tablespoon at a time until desired consistency is reached.
09 - Divide pasta among serving plates. Top with sliced blackened chicken. Garnish with chopped fresh parsley and additional grated Parmesan cheese.