Place the tomato halves, cut side up, on a greased baking sheet along with the onion slices and unpeeled garlic cloves.
Drizzle the oil and sprinkle the salt and pepper lightly over top. Sprinkle the sugar on just the tomatoes.
Bake at 375 degrees for 50-60 minutes or until the tomatoes are very soft and the onion is lightly browned.
Snip the ends off the garlic cloves, and squeeze the insides into the bowl of a food processor along with everything on the baking tray. Add 1 cup of stock, the basil, and vinegar. Process until smooth, adding more stock until the soup reaches preferred consistency.
Check for seasonings and serve hot or cold with optional toppings.