In a medium bowl, mix the softened butter, garlic, Dijon mustard, lemon juice, lemon zest, smoked paprika, red pepper flakes, parsley, chives, salt, and black pepper until smooth. Set aside.
Bring a large pot of salted water to a boil and cook the pasta until al dente. Reserve ½ cup of pasta water before draining.
Season the chicken with salt and black pepper.
Heat olive oil in a large skillet over medium-high heat. Cook the chicken until golden and cooked through.
Lower the heat and add half of the cowboy butter to the skillet. Once melted, stir in the heavy cream and let simmer gently until slightly thickened.
Add the cooked pasta and chicken to the skillet. Toss gently, adding pasta water as needed. Stir in Parmesan cheese until coated.
Remove from heat, garnish with extra parsley and Parmesan, and serve warm.