Boil the pasta: Cook the linguine in a large pot of salted boiling water until al dente. Reserve 1/2 cup of the pasta water, drain, and set aside.
Season the chicken: Rub both sides of the chicken breasts with blackened seasoning and smoked paprika, pressing it in to coat evenly.
Sear the chicken: Heat olive oil in a large skillet over medium-high heat. Add the chicken and cook for 5–6 minutes per side until it’s blackened and cooked through. Transfer to a plate and let it rest before slicing.
Make the creamy garlic sauce: Reduce heat to medium. In the same skillet, melt the butter and sauté the garlic for 1 minute. Pour in the chicken broth and simmer for 2 minutes, scraping up any bits from the pan.
Cream and cheese: Stir in the heavy cream and bring to a gentle simmer. Whisk in the Parmesan cheese until melted and smooth. Season with salt, pepper, and red pepper flakes if using.
Toss the pasta: Add the linguine and toss until evenly coated in the sauce. Use a splash of reserved pasta water to loosen if needed.
Serve: Slice the chicken and place it on top of the pasta. Garnish with chopped parsley and serve hot.