Bring a large pot of well-salted water to a boil. Blanch broccoli rabe until just tender, about 1 minute. Reserving cooking water, transfer broccoli to an ice-water bath until cool, then drain.
Pulse broccoli, pine nuts, and Parmesan in a food processor until coarsely chopped. Drizzle in 1/3 cup oil and process until smooth. Season with salt and red-pepper flakes.
Heat remaining 1 tablespoon oil in a large pan over medium-high heat. Brown sausage, turning, until cooked through, 5 to 7 minutes.
Meanwhile, cook pasta in reserved water according to package instructions. Drain, reserving 1 1/2 cups cooking water.
Toss pasta, pesto, and sausage, gradually adding cooking water until you get a creamy consistency. Serve with Parmesan and a drizzle of oil.