1. Heat oil in a 4-quart pot over moderate heat. Add the next 4 ingredients (through thyme); cover. Cook, stirring occasionally, about 16 minutes or until the onions begin to color.
2. Uncover and cook, stirring, 10 minutes or until onions are golden.
3. Stir in flour; cook for 2 minutes. Pour vermouth carefully into pan from measuring cup, scraping browned bits from bottom of pan. Cook 2 minutes more or until liquid is almost gone. Add broth, 2 cups water, Worcestershire, and Parmesan cheese. Bring to a simmer; cook 20 minutes.
4. Remove bay leaf, and ladle soup into bowls. Top each with sour cream and sprinkle of black pepper. Serve.
Time-saver alert! Make a double batch of this soup and freeze in an airtight container for up to three months. Just thaw, heat, and serve for a last-minute dinner.