Cook the pasta: Bring a large pot of salted water to a boil and cook linguine until al dente. Reserve 1/2 cup pasta water, then drain and set aside.
Sear the chicken: Season chicken strips with salt and pepper. In a large skillet over medium-high heat, heat olive oil. Add chicken and cook until golden brown and cooked through, about 6–8 minutes. Transfer to a plate.
Make cowboy butter: In the same skillet, melt butter. Add garlic and cook until fragrant, about 1 minute. Stir in Dijon mustard, lemon juice, red pepper flakes, smoked paprika, onion powder, and cayenne pepper.
Combine everything: Return chicken to the skillet. Add cooked linguine, reserved pasta water (as needed for consistency), Parmesan, and cream if using. Toss until the pasta is well coated and creamy.
Serve: Garnish with fresh parsley and additional Parmesan if desired. Serve hot.