Bring a large pot of salted water to a boil. Cook the pasta according to package directions until al dente. Drain and set aside.
Toss the chicken pieces with Cajun seasoning until evenly coated.
Heat olive oil in a large skillet over medium-high heat. Add the chicken and cook for 5–7 minutes, stirring occasionally, until browned and cooked through. Transfer the chicken to a plate and set aside.
In the same skillet, reduce heat to medium and add the butter. Once melted, stir in the minced garlic and cook for about 30 seconds until fragrant.
Pour in the heavy cream and bring to a gentle simmer. Add the softened cream cheese and whisk until smooth and fully incorporated.
Stir in mozzarella, parmesan, smoked paprika, and black pepper. Continue stirring until the cheeses melt and the sauce becomes thick and creamy.
Return the cooked chicken to the skillet and stir to coat in the sauce.
Add the drained pasta to the skillet and toss until everything is well combined and heated through.
Taste and adjust seasoning if needed. Serve hot.