Bring a large pot of salted water to a boil. Cook the bowtie pasta according to the package instructions until al dente, about 8-10 minutes. Add the broccoli florets in the last 2-3 minutes. Drain, reserving ½ cup of pasta water.

In a skillet, heat 2 tablespoons of olive oil over medium-high heat. Season chicken with Cajun seasoning, smoked paprika, salt, and pepper. Cook chicken for 5-7 minutes per side until golden brown and cooked through. Set aside.

In the same skillet, melt 4 tablespoons of butter over medium heat. Add minced garlic and red pepper flakes; sauté for about 1 minute. Stir in Dijon mustard, lemon juice, and zest; simmer for 1-2 minutes.

Return the sliced chicken to the skillet. Add drained pasta and broccoli, tossing everything together with the sauce. If dry, add reserved pasta water to coat.

Stir in grated Parmesan cheese, chopped parsley, and chives. Cook for another minute until cheese melts. Serve warm, topping with extra Parmesan if desired.