In a large, deep skillet, heat the olive oil. Add the sausage meat and cook over moderate heat, breaking up the meat with a wooden spoon, until no pink remains, about 4 minutes. Add the chopped onion and rosemary and cook over moderately low heat, stirring occasionally, until the onion is softened, about 6 minutes. Stir in the carrots and cook until heated through. Stir in the diluted tomato paste and season with salt and pepper. Remove from the heat, stir in the parsley and serve.