Wash and dry all produce. Bring a large pot of salted water to a boil. Cut any large broccoli florets into bite-size pieces. Remove sausage from casings.
Once water is boiling, add orecchiette to pot. Cook, stirring occasionally, until al dente, 9-12 minutes. Carefully scoop out and reserve ¼ cup pasta cooking water, then drain.
Heat a drizzle of olive oil in a large pan over medium heat. Add broccoli and 2 tsp water. Cover and steam 3 minutes. Uncover and increase heat to medium high. Cook, tossing occasionally, until browned and tender, 3-6 minutes more. Season with salt and pepper. Remove from pan and set aside.
Heat another drizzle of olive oil in same pan over medium-high heat. Add sausage, breaking up meat into pieces. Cook until crisp at edges and no longer pink, 4-5 minutes. Add a pinch of chili flakes (to taste) and cook another 30 seconds.
Add orecchiette, broccoli, pesto, pasta cooking water, and half the Parmesan to pan. Toss until everything is well coated and a thick sauce has formed, 1-2 minutes. Season with salt and pepper.
Divide orecchiette mixture between plates. Sprinkle with remaining Parmesan and serve.