3 cups (720 milliliters) broccoli, cut into florets, stems removed
1/4 cup (60 milliliters) olive oil, divided
3 garlic cloves, minced
3/4 teaspoon (4 milliliters) crushed red pepper
226 grams spicy or mild sausage, removed from casings and crumbled
285 grams rigatoni
1/2 cup (120 milliliters) Pecorino Romano, plus more for garnish
Boil the broccoli in a large pot of salted water until tender, about ten minutes. Using a slotted spoon, remove broccoli to a large bowl or another pot, reserving cooking water. Add two tablespoons (30 milliliters) olive oil to broccoli, then blitz with an immersion blender, adding some cooking water as you go, until sauce is smooth and bright green. Season with salt and set aside.
Add two tablespoons (30 milliliters) olive oil, minced garlic, and crushed red pepper to a large pan with high sides and heat over medium-high. Add crumbled sausage and cook until browned, stirring occasionally, about six to seven minutes.
Bring broccoli water back up to a boil, then add rigatoni and cook until al dente. Drain, reserving 1/2 cup (120 milliliters) of cooking water. Add pasta, broccoli pesto, Pecorino, and the reserved cooking water to pan with sausage, toss to combine, and heat through. Serve sprinkled with a generous amount of Pecorino.