Bring a large pot of salted water to the boil. Add orecchiette and cook until just shy of al dente. In the last 3 minutes of cooking, add broccoli florets and stems.
Meanwhile, heat 1 tbsp olive oil in a large pan over medium-high heat. Add sausage meat, breaking it up with a spoon, and cook until golden and cooked through (5–7 minutes).
Add remaining olive oil, garlic, fennel seeds, and chilli flakes. Cook 1–2 minutes until fragrant.
Using a slotted spoon, transfer the pasta and broccoli straight into the pan with the sausage. Add about ½ cup of the pasta cooking water along with the butter. Toss until a silky sauce clings to the pasta, adding more pasta water if needed.
Off the heat, stir through lemon zest and torn basil. Season with salt and pepper.
Serve immediately with grated Pecorino Romano.