In a soup pot, bring a few inches water to a boil, salt it, add the broccoli rabe and cook for 5 minutes. Drain the broccoli rabe and plunge into a bowl of ice water; drain again.
In the pot, heat 2 tablespoons EVOO over medium-high heat. Add the sausage, break up the meat and cook until browned. Add the onion and garlic and cook to soften, 5 minutes. Add the stock, cannellini beans, tomatoes and 1 cup water; season with salt and pepper. Cover the pot and bring to a boil. Stir in the pasta, lower the heat and simmer until al dente, 8 minutes. Turn off the heat and stir in the broccoli rabe. Top the stoup with the Pecorino Romano and a drizzle of EVOO.