Boil salted water in a large pot. Cook the linguine until al dente, according to package instructions. Reserve ½ cup of pasta water, then drain and set aside.

Season chicken breasts with salt, black pepper, smoked paprika, and red pepper flakes. Heat olive oil in a skillet over medium-high heat and cook chicken for 5-6 minutes per side, or until fully cooked. Remove from heat, let rest, then slice into bite-sized pieces.

Lower heat to medium and add butter to the same skillet. Stir in garlic and cook until fragrant (about 30 seconds). Add Dijon mustard, lemon juice, and chicken broth, scraping up browned bits from the pan. Simmer for 2-3 minutes.

Pour in heavy cream and stir well. Let simmer for another 2 minutes until slightly thickened. Add Parmesan cheese, stirring until melted and smooth. If needed, add a splash of reserved pasta water for consistency.

Add sliced chicken back to the skillet, followed by the drained linguine. Toss to coat the pasta evenly in the sauce. Cook for 1-2 more minutes to let flavors meld.

Remove from heat, sprinkle with fresh parsley, and serve immediately with extra Parmesan on top.