In a bowl, toss the chicken pieces with olive oil, Cajun seasoning, and smoked paprika until evenly coated. Let rest for 5 minutes.

Bring a large pot of salted water to a boil. Add spaghetti and cook until al dente, about 9–11 minutes. Reserve 1/2 cup pasta water, then drain and set aside.

While pasta cooks, heat a large skillet over medium-high heat. Add the seasoned chicken and cook for 6–8 minutes, stirring occasionally, until browned and cooked through. Remove chicken and set aside.

In the same skillet, reduce heat to medium. Add butter and let melt. Add minced garlic and cook for 30–60 seconds until fragrant—don’t let it burn.

Sprinkle the flour over the butter-garlic mixture and whisk constantly for 1 minute to cook out the raw flour taste.

Gradually whisk in milk and chicken broth until smooth. Bring to a gentle simmer and cook for 3–4 minutes until the sauce thickens slightly. If too thick, add a splash of reserved pasta water.

Lower heat and add cream cheese; stir until completely melted and creamy (about 2–3 minutes). Stir in 1½ cups mozzarella and all the Parmesan until melted. Taste and season with salt, pepper, and red pepper flakes if using.

Add the cooked spaghetti and chicken back to the skillet. Toss thoroughly to coat every strand with that garlicky, cheesy sauce—about 1–2 minutes. If sauce is too tight, loosen with reserved pasta water, 1 tablespoon at a time.

Transfer to an oven-safe dish, sprinkle remaining 1/2 cup mozzarella on top, and broil for 2–3 minutes until bubbly and golden. Watch closely to avoid burning.

Garnish with parsley or green onions and a squeeze of lemon if you like a bright finish. Serve immediately.