Bring a large pot of salted water to a boil. Add the linguine and cook according to package instructions until al dente, about 8-10 minutes. Reserve 1 cup of pasta water before draining.

Season both sides of the chicken breasts with salt and pepper. Heat olive oil in a skillet over medium heat. Cook chicken for 5-7 minutes on each side until golden brown. Remove from heat.

In the same skillet, reduce heat to medium-low and add butter. Once melted, add minced garlic and stir for 1-2 minutes until fragrant. Mix in Dijon mustard, paprika, and optional red pepper flakes.

Pour in heavy cream and chicken broth, stirring until the sauce is smooth and creamy. Return cooked chicken to skillet and let simmer for 2-3 minutes.

Add drained linguine into the skillet and toss gently until coated. Add reserved pasta water as needed to achieve desired consistency.

Remove from heat, stir in fresh parsley and grated parmesan cheese. Serve immediately, garnished with extra parsley and parmesan.