Heat oil in skillet over medium-high heat until just smoking. Add sausage and cook, breaking up meat with wooden spoon until lightly browned, about 5 minutes. Add shallots and cook until softened, about 2 minutes. Stir in garlic and oregano and cook until fragrant, about 30 seconds. Stir in beans and cook until heated through, about 2 minutes; set aside.
Meanwhile, bring 4 quarts water to boil in large pot. Add broccoli rabe and 1 tbsp salt and cook, stirring often, until crisp-tender, about 2 minutes. Using slotted spoon, transfer broccoli rabe to skillet with sausage and bean mixture.
Return water to boil, add pasta and cook, stirring often, until al dente. Reserve 1 cup of cooking water, then drain pasta and return it to pot. Add sausage-bean-broccoli rabe mixture, Parmesan, and ⅓ cup reserved cooking water and toss to combine. Season with salt and pepper to taste and adjust consistency with remaining ⅔ cup reserved cooking water as needed. Serve