Heat the oil in a large saucepan or soup pot over medium heat. Once it shimmers, add the onion and cook, stirring often, until lightly browned, 5 to 7 minutes. Stir in the garlic and cook until fragrant, about 30 seconds. Turn off the heat.
Place the chicken (or vegetable) broth, tomatoes, vermouth, tomato paste, salt, dried basil, fennel seeds, oregano, thyme, pepper, sugar, fresh basil, and the sautéed onion and garlic in the blender. Select the SOUP setting. Once the cycle finishes, divide the soup among bowls. Sprinkle goat cheese over the top and serve.