Orecchiette with Broccoli and Sausage

From the garden

• 1 lb broccoli, cut into small florets, stems peeled and diced
• 4 cloves garlic, thinly sliced

From the pantry

• 12 oz orecchiette or other short pasta
• 1 lb Italian sausage, casings removed
• ½ tsp red pepper flakes
• 2 tbsp olive oil
• ¾ cup grated parmesan — plus more for serving
• salt — for the pasta water and to taste
• black pepper

1. Bring a large pot of well-salted water to a boil and cook the pasta. Three minutes before it's done, add the broccoli right into the pot — it should end up very tender, on the edge of falling apart, which is exactly what you want here.
2. Meanwhile, heat the olive oil in a wide skillet over medium-high heat and brown the sausage, breaking it into bite-size crumbles, until deeply golden with crisp edges, 6–8 minutes.
3. Push the sausage aside, drop the heat to medium, and cook the garlic and red pepper flakes in the fat until fragrant and just golden at the edges, about 1 minute.
4. Scoop out 1 cup of pasta water, then drain the pasta and broccoli and tip them into the skillet. Toss over medium heat, mashing some of the broccoli into the fat so it starts coating the pasta like a sauce.
5. Off the heat, add the parmesan and a splash of pasta water and toss hard until glossy, adding more water as needed. Season with black pepper and serve with extra parmesan.