Cook pasta according to the package directions, adding broccoli during the last 5-6 minutes of cooking. Drain well and cover to keep warm.
Meanwhile, heat a large skillet over medium heat. Dice onion.
Remove casings from the sausage; cook together with the onion until meat is no longer pink, breaking the meat up with a spatula as it cooks. Drain any excess fat.
Mince garlic and add to the skillet; cook and stir 1 minute. Meanwhile, zest 2 teaspoons of the lemon peel.
Add sausage mixture, lemon peel, and black pepper to the cooked pasta; toss until well blended.
Add the cheese and toss once more, allowing the cheese to melt.
Sprinkle each serving with additional cheese if desired; serve grapes on the side.