Bring a large pot of salted water to a boil. Add the bowtie pasta and cook until al dente, about 8-10 minutes. In the last 3 minutes, stir in the broccoli florets. Reserve about a cup of the pasta water, then drain the pasta and broccoli.

Season the chicken with Cajun seasoning on both sides. In a large skillet, heat olive oil over medium-high heat. Sauté the chicken for about 6-7 minutes per side, until golden brown and cooked through. Remove from skillet and let it rest.

In the same skillet, reduce heat to medium and add unsalted butter. Once melted, add minced garlic and sauté for about 30 seconds. Stir in crushed red pepper flakes, Dijon mustard, lemon juice, and lemon zest, mixing well.

Add the drained bowtie pasta and broccoli back into the skillet, along with the cooked chicken. Toss together in the cowboy butter sauce, adding reserved pasta water gradually to reach desired creaminess. Stir in freshly grated Parmesan cheese until melted.

Serve on plates, topped with additional Parmesan cheese, parsley, and chives. Squeeze a little fresh lemon juice over the top before serving.