Boil the pasta: Bring a large pot of salted water to a boil.
Cook pasta until just shy of al dente. Reserve 1/2 cup pasta water and drain.
Season the chicken: Pat chicken dry. Toss with Cajun seasoning, smoked paprika, garlic powder, salt, and pepper until evenly coated.
Sear the chicken: Heat olive oil in a large skillet over medium-high.
Add chicken in a single layer and cook 3–4 minutes per side until browned and cooked through. Transfer to a plate.
Start the sauce: Reduce heat to medium. Add butter to the same skillet.
Stir in garlic and cook 30 seconds until fragrant, scraping up browned bits.
Creamy base: Pour in heavy cream and milk. Simmer gently for 2–3 minutes, stirring. Do not boil.
Add cheese: Off heat or on low, whisk in Parmesan until melted and smooth.
If thick, loosen with a splash of reserved pasta water.
Combine: Add pasta and chicken to the skillet. Toss until coated and glossy. Add a squeeze of lemon if using, and adjust salt, pepper, and Cajun seasoning.
Finish: Sprinkle red pepper flakes for extra heat.
Garnish with parsley or green onions. Serve hot.