Bring a large pot of salted water to a boil. Cook farfalle pasta according to package instructions for al dente. Add broccoli florets to the boiling water during the final 3 minutes of cooking. Drain and set aside.
Season chicken cubes with 1/2 teaspoon salt and 1/4 teaspoon black pepper.
In a large skillet over medium-high heat, add olive oil. Sauté chicken until golden brown and cooked through (internal temperature 165°F), approximately 6-8 minutes. Remove chicken from skillet and set aside.
In the same skillet, reduce heat to low and add the butter. Once melted, stir in the minced garlic and cook for 1 minute until fragrant.
Whisk in the Dijon mustard, red pepper flakes, smoked paprika, lemon juice, and lemon zest until emulsified.
Incorporate the fresh parsley and chives into the butter mixture.
Return the cooked pasta, broccoli, and chicken to the skillet. Toss thoroughly to coat all components in the cowboy butter sauce.
Adjust seasoning with remaining salt and pepper to taste and serve immediately.