Bring a large pot of salted water to a boil. Add the linguine and cook according to package instructions until al dente, about 9-11 minutes. Reserve 1 cup of pasta water before draining.

Heat a large skillet over medium-high heat, add olive oil, season chicken with salt and pepper, and sear for 6-7 minutes on each side until cooked through. Remove and let it rest.

In the same skillet, melt butter, add garlic, Dijon mustard, paprika, and optional red pepper flakes, stirring until fragrant for about 1-2 minutes.

Stir in lemon juice, heavy cream, and chicken broth or reserved pasta water until smooth. Simmer for 2-3 minutes.

Slice chicken and return to the skillet with drained linguine and chopped parsley. Mix well and adjust sauce consistency with reserved pasta water if needed. Serve hot, garnished with parmesan cheese.