Boil a large pot of water over high heat, add linguine and cook according to package instructions until al dente, about 8-10 minutes. Reserve 1 cup of pasta water before draining.

In a large skillet, heat 2 tablespoons of olive oil over medium-high heat. Add chicken and sear for 5-7 minutes per side until golden and cooked through. Transfer to a cutting board and let rest before slicing.

In the same skillet, melt 2 tablespoons of butter. Add minced garlic and sauté until fragrant. Stir in Dijon mustard, paprika, and red pepper flakes (if using) for another minute.

Pour in heavy cream and chicken broth, stirring gently. Increase heat and simmer for 3-5 minutes until slightly thickened. Adjust seasoning with salt and pepper.

Add sliced chicken and linguine to the skillet, tossing to coat. Add reserved pasta water gradually if mixture is too thick.

Remove from heat and stir in lemon juice, zest, and parsley. Top with grated Parmesan cheese and serve immediately.