Cook the pasta according to the package directions, adding the broccoli during the last minute. Drain and return the pasta and broccoli to the pot.
Meanwhile, heat 1 tablespoon of the oil in a large skillet over medium-high heat. Add the turkey, garlic, fennel seed, and red pepper and cook, breaking up the meat with a spoon, until browned, 3 to 5 minutes; season with ½ teaspoon salt.
Toss the turkey mixture with the pasta and broccoli and the remaining 2 tablespoons of oil. Serve with Parmesan.