Bring a large pot of salted water to a boil and cook bowtie pasta until al dente. Add broccoli florets during the final few minutes so they cook until tender but still bright green. Reserve half a cup of pasta water before draining to help create a smooth sauce later.
Season chicken pieces with Cajun seasoning, garlic powder, smoked paprika, salt, and pepper. Heat olive oil in a skillet over medium-high heat and cook chicken until golden and fully cooked. Keep the browned bits in the pan since they add extra flavor to the sauce.
Lower the heat and melt butter in the same skillet. Add minced garlic and cook briefly until fragrant, then stir in red pepper flakes if using. Mix in Dijon mustard, lemon juice, and zest before finishing with fresh parsley and chives for brightness.
Return cooked chicken to the skillet and add drained pasta and broccoli. Toss everything together so the sauce coats every ingredient evenly. Add reserved pasta water gradually until the sauce becomes silky and smooth.
Stir in grated Parmesan cheese until melted and blended into the sauce. Taste and adjust seasoning if needed. Serve warm with extra cheese and a fresh squeeze of lemon for added brightness.