Rinse the broccoli rabe and pat dry. Cut off most of the stems (the thickest parts). Using a vegetable peeler, pull some skin off the stems, and continue to until you hit the leaves. Chop into 1-inch pieces and set aside.

Place a large skillet over medium heat. When water flicked onto the skillet sizzles, add the sausage and oregano and cook, breaking up the meat with a wooden spoon, for 6 to 8 minutes or until browned and cooked through. Using tongs or a slotted spoon, transfer the sausage to a plate.

Immediately add the broccoli rabe, parsnip noodles, garlic, and red pepper flakes to the skillet. Season with salt and black pepper, then add the broth. Cook until the broth has reduced and the parsnip noodles are al dente, about 5 minutes.

Return the sausage to the skillet, add the cheese, and stir to combine. Remove from the heat and toss the ingredients to combine fully.

Divide among four plates, garnish with the parsley, and serve.