Bring a large pot of salted water to a rapid boil. Add trimmed broccoli rabe, then cook. Use tongs or a slotted spoon to transfer to an ice bath, then return the water to a boil.
Add orecchiette pasta to the boiling water and cook according to package directions until al dente. Before draining, reserve the pasta cooking water.
In a large skillet, heat olive oil over medium-high heat. Add sausage, breaking up with a spatula, then cook until browned on all sides. Add chopped garlic and crushed red pepper flakes, then cook.
Drain the broccoli rabe, then give it a rough chop so it’s in manageable bite-size pieces. Add broccoli rabe and cooked pasta to the Italian sausage. Stir in grated Parmesan (or Pecorino) and reserved pasta water, then taste and adjust seasoning as needed.
Serve in bowls with a drizzle of olive oil, additional grated cheese, a pinch of flaky sea salt, and lots of freshly ground black pepper.