Boil linguine in salted water according to package directions. Reserve ½ cup pasta water before draining.
Heat olive oil in a skillet over medium-high. Season chicken with salt and pepper, cook for 5–7 minutes until golden and fully cooked. Remove and set aside.
In the same skillet, melt butter. Add garlic, paprika, and red pepper flakes. Cook for 1 minute until fragrant.
Stir in Dijon mustard, lemon juice, zest, and chicken broth (or pasta water). Scrape the skillet to release browned bits.
Add heavy cream and half the parsley. Cook 2 minutes until slightly thickened.
Return chicken to the skillet. Add linguine, parmesan, and pasta water if needed. Toss to coat.
Season to taste. Garnish with parsley and extra parmesan. Serve hot.