Heat the oil in a large heavy skillet over medium heat. Add the sausage and cook, stirring occasionally, until brown, about 7 minutes. Push to one side of the skillet and increase the heat to high. Add the tomatoes, stirring to break them up a bit, and cook until the edges brown and the oil turns red, about 6 minutes. Stir the sausage and tomatoes together.
Add the garlic, bay leaves, fennel seeds and red pepper flakes to the skillet, then scatter the saffron over the mixture. Cook, stirring, about 2 minutes. Add the parsley, 1 cup basil and 1 teaspoon salt. Reduce the heat to medium and cook, stirring occasionally, about 15 minutes.
Remove and discard the bay leaves.
Meanwhile, cook the spaghetti in a large pot of salted boiling water until al dente. Drain, reserving 1/2 cup pasta water. Add the spaghetti, cooking liquid and reserved tomato juice to the sausage sauce and toss, about 3 minutes. Top with the pecorino and the remaining 1/2 cup basil.