Boil the pasta in salted water. During the last 3 minutes of cooking, add the broccoli florets to the same pot, then drain both together.
Heat the olive oil in a skillet over medium-high heat. Season the chicken with salt and pepper, cook until browned and cooked through, then remove to a plate.
Melt the butter in the same skillet over medium-low heat. Stir in the garlic, Dijon mustard, red pepper flakes, and paprika, cooking for 1 minute.
Remove the pan from the heat. Stir in the parsley, chives, lemon zest, and lemon juice to complete the sauce.
Return the cooked chicken to the pan, add the drained pasta and broccoli, and toss everything well to coat.
Sprinkle with Parmesan cheese, toss once more, and serve immediately.
