Boil a large pot of salted water. Cook the linguine according to package instructions until al dente, usually around 8–10 minutes. Reserve a cup of pasta water before draining.

In a large skillet, heat olive oil and butter over medium heat. Cook the chicken for about 6-7 minutes on each side until golden brown and cooked through. Remove the chicken and let it rest before slicing.

In the same skillet, add the minced garlic and sauté for about 1 minute. Stir in Dijon mustard, paprika, and red pepper flakes (if using), cook for another minute.

Lower the heat to medium-low and add the heavy cream, lemon juice, and zest. Stir well and let it simmer for about 3-4 minutes until thickened.

Add the cooked linguine to the skillet, tossing to coat evenly. Use reserved pasta water to adjust the sauce consistency if needed.

Slice the chicken and place it on top of the linguine. Sprinkle with parmesan cheese and fresh parsley. Serve hot.