Bring a large pot of well-salted water to a boil. Cook bowtie pasta according to package directions until al dente. During the last 3 minutes of cooking, add the broccoli florets to the same pot. Reserve 1/2 cup of pasta water before draining. Drain and set aside.

Season chicken pieces with Cajun seasoning, garlic powder, smoked paprika, salt, and pepper. Toss until every piece is evenly coated.

Heat olive oil in a large skillet over medium-high heat. Add chicken in a single layer and sear undisturbed for 2 to 3 minutes before turning. Cook until golden and cooked through, about 6 to 7 minutes total. Remove chicken and set aside, leaving browned bits in the pan.

Lower heat to medium and add butter to the skillet. Once melted, scrape up the browned bits from the bottom of the pan. Add minced garlic and cook until fragrant, about 1 minute.

Stir in red pepper flakes, Dijon mustard, lemon juice, and lemon zest. Season with salt and pepper. Stir in parsley and chives.

Return the chicken, pasta, and broccoli to the skillet. Toss gently to coat everything in the sauce. Add reserved pasta water a splash at a time until the sauce is silky and clings to the pasta.

Stir in Parmesan cheese until melted and creamy. Serve warm topped with extra Parmesan, fresh herbs, and a squeeze of lemon if desired.