01 - Bring a large pot of salted water to a boil. Add linguine and cook until al dente according to package directions. Reserve 0.5 cup of pasta cooking water, then drain pasta and set aside.
02 - Pat chicken breasts dry and season both sides with salt, black pepper, smoked paprika, and red pepper flakes. Heat olive oil in a large skillet over medium-high heat. Add chicken and cook for 5 to 6 minutes per side, until fully cooked. Remove chicken to a plate and let rest before slicing into bite-sized strips.
03 - Reduce heat to medium and add butter to the same skillet. Once melted, add minced garlic and sauté for 30 seconds until aromatic. Stir in Dijon mustard, lemon juice, and chicken broth, scraping up any browned bits at the bottom. Simmer for 2 to 3 minutes for flavors to meld.
04 - Pour heavy cream into the skillet and stir thoroughly. Allow sauce to simmer for 2 minutes until it begins to thicken. Add grated Parmesan cheese, stirring until the cheese melts and the sauce becomes smooth. Add a splash of reserved pasta water to achieve desired consistency, if necessary.
05 - Return sliced chicken to the skillet, followed by the drained linguine. Toss everything together to ensure the pasta is evenly coated in sauce. Cook for 1 to 2 minutes to finish melding flavors.
06 - Remove skillet from heat. Sprinkle chopped fresh parsley over the pasta and serve immediately, topping with additional Parmesan cheese if desired.