First, prepare the broccoli rabe by trimming the stems to remove as much of the tough stalk as possible, about 1-2 inches. Submerge the broccoli rabe in a large bowl of cold water and remove any discolored leaves or debris. Rinse it thoroughly in a colander under running water.
Blanch the broccoli rabe by plunging it into boiling water and simmering for 2-3 minutes. Save a cup of the blanching water to use later for the sauce. Drain the broccoli rabe and immediately plunge it into a bowl of ice water to stop it from overcooking.
In a separate pot, cook the orecchiette pasta in salted boiling water (about 4 quarts water and 2 tablespoons salt) until it's al dente. Drain the pasta but reserve the cooking water.
Next, prepare the sausage by removing the casing and crumbling it into small pieces.
Heat olive oil in a large skillet over medium heat, then add the crumbled sausage. Cook the sausage, occasionally stirring, until it's browned.
Once the sausage is cooked, add the thinly sliced garlic cloves to the skillet and cook for 1-2 minutes until the garlic is fragrant and slightly golden in color.
Add the blanched broccoli rabe to the skillet with sausage and garlic. Cook them together until the broccoli becomes tender and the flavors meld, about 5 minutes.
Combine the orecchiette pasta, sausage, and broccoli rabe mixture by gently tossing them together in the skillet. You may need to add some of the reserved pasta cooking water to help create a sauce. Season the dish with salt and pepper to taste.
Serve the orecchiette dish in individual bowls and top with grated Parmigiano-Reggiano cheese. Enjoy your delicious Italian pasta dish, which showcases the perfect combination of orecchiette pasta, Italian sausage, and broccoli rabe.