Heat the oil over moderate heat in a large frying pan. Add the sausage and cook for about 8 minutes or cooked through. Once the sausage is done, remove from pan and cut into 1/2-inch slices when cool enough to handle.
Add the chopped onion, peppers, and 3/4 teaspoon of the salt to the pan. Cook, stirring occasionally, until the vegetables begin to brown. Cover and cook, stirring occasionally until the vegetables have softened. Add the garlic and cook, stirring, for about 30 seconds. Add the tomatoes, broth, vermouth, sausage, 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 rest of ingredients Serve with Parmesan.