Bring a large pot of salted water to a rolling boil and add the linguine. Cook according to package directions until al dente, usually about 8-10 minutes. Reserve ½ cup of pasta water before draining the linguine.

In a large, deep skillet, heat 2 tablespoons of olive oil over medium heat. Season the chicken breasts with salt and pepper and sauté for 6-7 minutes per side until golden brown and cooked through. Remove and let rest.

In the same skillet, melt 4 tablespoons of butter. Add the minced garlic and sauté for 1-2 minutes until fragrant. Mix in the Dijon mustard, paprika, and red pepper flakes for another minute.

Pour in the heavy cream and stir gently to combine. Gradually add the grated Parmesan cheese, mixing until it melts and creates a smooth sauce. Use reserved pasta water to adjust thickness as needed.

Return the cooked chicken to the skillet, chop it into pieces, then add the drained linguine. Toss everything together, ensuring the pasta is thoroughly coated with sauce.

Garnish with chopped fresh parsley and serve immediately with a light salad or garlic bread.