Sausage and Peppers Pasta With Broccoli

INGREDIENTS
¼ cup extra-virgin olive oil
1 pound sweet Italian pork sausage, casings removed
1 pound broccoli, cut into 1 1/2-inch florets (about 4 cups)
2 medium yellow bell peppers (12 ounces), cored, seeded and thinly sliced (about 2 1/2 cups)
3 cloves garlic, thinly sliced
 Kosher salt and pepper
1 pound rigatoni
½ cup grated Parmesan (2 ounces), plus more for serving
2 tablespoons fresh lemon juice (from about 1/2 lemon)
½ teaspoon red-pepper flakes

Heat 2 tablespoons oil in a large nonstick skillet over medium heat. Add the sausage and cook, breaking up the meat using a wooden spoon, until browned, about 5 minutes. Scrape the mixture into a medium bowl. Add the remaining 2 tablespoons oil, the broccoli, peppers and garlic to the skillet and season with salt and pepper. Cook, stirring often, until they soften and begin to brown, about 8 minutes.

Meanwhile, cook the pasta in a large pot of boiling salted water until al dente. Reserve 1 cup cooking water and drain the pasta. Return the pasta and reserved cooking water to the pot over low heat. Add the broccoli mixture, cooked sausage and its accumulated juices, 1/2 cup Parmesan, the lemon juice and red-pepper flakes and stir vigorously until liquid is slightly thickened and saucy, about 2 minutes.
Season with salt and pepper.

Serve the pasta with additional Parmesan for sprinkling on top.