Cook the pasta: Bring a large pot of heavily salted water to a boil over high heat. Add the orecchiette and cook until al dente, about 1 minute less than the package instructions. Reserve 2 cups of pasta water and set aside. Using a spider skimmer or colander, remove the pasta from the pot, but keep the boiling water for blanching the broccoli rabe.
Blanch the broccoli rabe: Add the broccoli rabe stalks (with florets attached) to the boiling water and cook until barely tender, 1 minute 30 seconds to 2 minutes. Remove using a slotted spoon and transfer to a plate. Add the rabe leaves to the boiling water and cook for another minute until just wilted. Drain and set aside. Once cooled slightly, chop the stalks and florets into 1 ½-inch pieces and combine with the blanched leaves.
Cook the sausage: Heat the olive oil in a large skillet over medium heat until shimmering. Break the sausage into small bite-sized pieces and add them to the skillet in a single layer. Let cook undisturbed until the bottom side is golden brown, about 2 minutes. Using a spoon or spatula, flip the sausage pieces and continue cooking until browned on all sides.
Sauté the aromatics: Add the garlic and red pepper flakes to the skillet and cook, stirring, until fragrant, about 30 seconds.
Deglaze with wine: Increase the heat to medium-high and pour in the white wine, scraping up any browned bits from the bottom of the pan. Let it simmer and reduce slightly, about 30 seconds. Turn off the heat.
Combine the ingredients: Return the skillet to high heat and add 1 cup of the reserved pasta water along with the blanched broccoli rabe. Bring to a boil, stirring constantly, until the water emulsifies with the oil and creates a sauce, about 1-2 minutes.
Finish the dish: Add the orecchiette to the skillet and toss everything together, allowing the pasta to absorb the flavors. If the sauce is too thick, add more reserved pasta water in ¼ cup increments as needed to keep it slightly loose.
Add cheese and serve: Remove from heat and stir in ¾ of the grated Pecorino Romano, mixing well to incorporate. Season with salt to taste. Serve immediately, passing the remaining cheese at the table.