1. Bring a large pot of salted water to a boil. Add the bowtie pasta and cook according to package directions. During the last 2 minutes of cooking, add the broccoli florets to the pot. Drain the pasta and broccoli, then set them aside.

2. Heat the olive oil in a large skillet over medium-high heat. Add the chicken pieces, season with salt and pepper, and cook until browned and cooked through. Remove the chicken from the skillet and set it aside.

3. Reduce the heat in the skillet to medium. Melt the butter, then add the garlic and sauté for 1-2 minutes until fragrant. Stir in the red pepper flakes (if using), Dijon mustard, lemon juice, and lemon zest. Pour in the chicken broth and simmer for 2 minutes.

4. Stir in the heavy cream and Parmesan cheese. Simmer for 1-2 minutes, allowing the sauce to thicken slightly.

5. Return the cooked chicken to the skillet. Add the cooked pasta and broccoli, tossing everything to coat evenly in the creamy cowboy butter sauce.

6. Stir in the chopped fresh parsley. Taste the dish and adjust the seasoning with additional salt, pepper, or lemon as needed.