How to Make It
In a large frying pan, heat the oil over moderate heat. Add the sausage and cook, turning, until browned and cooked through, about 8 minutes. Remove. When the sausage is cool enough to handle, cut it into 1/2-inch slices.
Add the onion, peppers, and 3/4 teaspoon of the salt to the pan. Cook, stirring frequently, until the vegetables begin to brown, about 5 minutes. Cover and cook, stirring occasionally until the vegetables are soft, about 3 minutes longer. Add the garlic and cook, stirring, for about 30 seconds. Add the tomatoes, broth, vermouth, the reserved sausage and any accumulated juices, the parsley, and the remaining 1 teaspoon salt and bring to a simmer.
In a large pot of boiling, salted water, cook the spaghetti until just done, about 12 minutes. Drain and toss with the sausage-and-pepper mixture and the Parmesan. Serve with additional Parmesan.