Bring a large pot of salted water to a rolling boil. Cook the linguine according to package instructions until al dente, about 8-10 minutes. Reserve about a cup of pasta water before draining. Drain pasta and set aside.

In a large skillet, heat olive oil over medium-high heat. Add chicken breasts and cook for about 6-8 minutes per side until golden brown and cooked through. Remove chicken and let rest before slicing into bite-sized pieces.

In the same skillet, melt butter over medium heat. Add minced garlic and sauté for about 1 minute. Stir in Dijon mustard, paprika, and red pepper flakes (if using) to create a flavorful base. Stir for another minute.

Pour in heavy cream and chicken broth, bringing mixture to a gentle simmer. Let the sauce reduce for about 3-5 minutes. Add cooked linguine, tossing to coat in the sauce, and stir in reserved pasta water as needed for consistency.

Stir in lemon juice, zest, and grated Parmesan cheese. Mix well and season with salt and black pepper. Allow to heat on low for another 2-3 minutes.

Remove from heat and fold in chopped parsley. Serve hot, garnished with extra parsley and Parmesan if desired.