Season the chicken breasts with salt, pepper, and 1 tablespoon of Cajun seasoning on both sides.
Heat olive oil in a large skillet over medium-high heat. Sear the chicken for 6-7 minutes per side until golden and cooked through; remove and let rest.
While chicken cooks, bring a large pot of salted water to a boil. Cook pasta according to package directions until al dente, reserving 1 cup pasta water before draining.
Slice the rested chicken into strips or bite-sized pieces.
In the skillet used for chicken, melt butter over medium heat. Add minced garlic and sauté 1-2 minutes until fragrant.
Add Cajun seasoning and smoked paprika to the skillet. Stir and cook spices for 1 minute.
Pour in heavy cream and chicken broth, stirring to combine. Simmer for 4-5 minutes until sauce slightly thickens.
Stir in grated Parmesan until fully melted. Adjust seasoning with salt, pepper, or extra Cajun seasoning as desired.
Add cooked pasta to the sauce, tossing to coat. Thin sauce with reserved pasta water if needed.
Add sliced chicken to the skillet and mix well to combine.
Remove from heat and garnish with chopped fresh parsley and extra Parmesan if desired. Serve immediately.