Cook the broccoli rabe in a large pot of boiling salted water until crisp tender, about 1 minute. Transfer the broccoli rabe to a large bowl of ice water to cool, saving the cooking water. Bring the reserved cooking water back to a boil.
Heat the oil in a heavy large skillet over medium heat. Add the sausage and cook, breaking it up into pieces with a spoon, until browned and juices form, about 12 minutes. Add the garlic and red pepper flakes, and saute until fragrant, about 2 minutes.
Meanwhile, when the reserved cooking water is boiling, add the orecchiette and cook until al dente, tender but still firm to the bite, stirring occasionally, about 8 minutes.
Strain the broccoli rabe and add it to the pan with the sausage mixture and toss to coat with the juices. Add the pasta to the skillet. Stir in the Parmesan and serve immediately.
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