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.
1. I used 1 large summer squash instead of parsnips, so I omitted the chicken broth step!
2. If you don’t like the bitterness of broccoli rabe, try parboiling it after trimming. Bring a large pot filled halfway with water to a boil, add the broccoli rabe, cook for 3 minutes, then transfer to a bowl of ice water. Otherwise, broccolini or plain broccoli are great choices with similar textures.