Preheat the oven to 425 degrees . On a baking sheet, toss the sausage, fennel, onion and carrots with the olive oil; season with salt and pepper. Cook until the vegetables are tender, about 30 minutes.
Meanwhile, in a large pot of boiling, salted water, cook the pasta until al dente; drain, reserving 1/3 cup of the pasta cooking water. Transfer the pasta to a large bowl.
Add the sausage-vegetable mixture to the pasta. Add the reserved pasta cooking water to the baking sheet, scraping up any browned bits; transfer to the pasta mixture. Toss in the parsley; season with salt and pepper.