Bring a large pot of salted water to a boil. Add the linguine pasta and cook according to package instructions until al dente, around 8–10 minutes. Drain, reserving ½ cup of starchy pasta water.

In a large skillet, heat olive oil and butter over medium-high heat. Add minced garlic and sauté for about 30 seconds until fragrant. Add chicken, seasoning with salt and pepper, and cook for 6–7 minutes on each side until golden brown. Remove and slice into bite-sized pieces.

In the same skillet, lower the heat and stir in Dijon mustard, paprika, and optional red pepper flakes. Cook for 1 minute. Add lemon juice and zest, scraping up browned bits. Pour in chicken broth and heavy cream, stirring to combine. Let simmer for 3–5 minutes until slightly thickened.

Return sliced chicken to skillet, mixing it with the sauce for about 2 minutes. Add cooked linguine, tossing until evenly coated. Gradually stir in reserved pasta water if sauce is too thick.

Remove from heat and plate the Cowboy Butter Chicken Linguine. Garnish with parsley and Parmesan cheese, and serve with garlic bread on the side.