Heat the olive oil in a Dutch oven over medium heat. Add onion and garlic, and cook for 10 minutes, stirring frequently. Stir in the water and the next 5 ingredients (water through tomatoes), and bring to a boil. Reduce heat, and simmer 20 minutes.
Place 2 cups soup in a blender or food processor, and process until smooth. Pour the pureed soup into a bowl. Repeat procedure with 2 cups soup. Return all pureed soup to pan. Stir in the vinegar, and bring to a boil. Remove from heat. Spoon 1 1/2 cups soup into each of 6 bowls; sprinkle each serving with 1 tablespoon cheese.