Bring a large pot of salted water to a boil. Cook the bowtie pasta according to package instructions until al dente.
Add the broccoli florets during the last 3 minutes of cooking. Reserve 1/2 cup of pasta water, then drain the pasta and broccoli.
Season the chicken pieces with Cajun seasoning, garlic powder, smoked paprika, salt, and black pepper.
Heat olive oil in a large skillet over medium-high heat. Cook the chicken for 6–7 minutes until golden brown and fully cooked. Remove from the skillet and set aside.
Reduce heat to medium and add butter to the same skillet. Once melted, stir in minced garlic and cook for about 1 minute until fragrant.
Add crushed red pepper flakes, Dijon mustard, lemon zest, and lemon juice. Stir well and season lightly with salt and pepper.
Return the chicken to the skillet along with the cooked pasta and broccoli. Toss everything together until evenly coated in the cowboy butter lemon sauce.
Add reserved pasta water a little at a time until the sauce reaches your desired consistency.
Stir in Parmesan cheese until melted and creamy.
Serve Cowboy Butter Lemon Bowtie Chicken warm with extra Parmesan cheese and fresh herbs on top.