Bring a pot of water to a boil; add a generous amount of salt. Add the orecchiette and cook to al dente (take 3 minutes off of the time on the box; it'll finish cooking later). Reserve 1/2 cup of the pasta water, then drain.
Heat a large skillet over medium-high heat. Add the sausage and cook, breaking it up with a wooden spoon, until brown, about 7 minutes. Use a slotted spoon to transfer the sausage to a plate, keeping the fat in the skillet. Add the garlic and cook for 30 seconds. Add the broccolini and cook until crisp-tender, about 7 minutes. Reduce the heat to medium low. Add the pasta and sausage to the skillet along with the Parmesan, lemon zest and juice, a couple of pinches of crushed red pepper and a bunch of turns of black pepper. Stir in a few tablespoons of the pasta water and continue to cook, stirring, until glossy, adding more pasta water if needed. Taste and adjust the seasoning as desired. Sprinkle with more Parmesan before serving.