Cook the Pasta: Bring a large pot of salted water to boil. Add the bowtie pasta and cook according to package directions until al dente. During the last 3 minutes of cooking, add the broccoli florets to blanch them. Drain and set aside.

Cook the Chicken: Season chicken pieces with salt, pepper, and oregano. Heat olive oil in a large skillet over medium-high heat. Add chicken and cook until golden brown and cooked through, about 6-8 minutes. Remove chicken from skillet and set aside.

Make the Cowboy Butter Sauce: In the same skillet, reduce heat to medium. Add butter and minced garlic. Cook for 1 minute until fragrant. Add lemon juice, lemon zest, smoked paprika, and red pepper flakes. Stir in chicken broth and heavy cream, simmering for 2-3 minutes until slightly thickened.

Combine Everything: Return the cooked chicken to the skillet. Add the drained pasta and broccoli. Toss everything together until well coated in the sauce. Cook for another 2 minutes to heat through.

Serve: Garnish with fresh parsley and grated Parmesan cheese. Serve immediately while hot.