Place the tomato halves, cut side up, on a baking tray with the garlic cloves. Drizzle with the oil, and sprinkle with salt and pepper. Roast at 375 degrees F (195 degrees C) for 1 hour.
Snip the ends off the garlic cloves, and squeeze the insides into the bowl of a food processor along with the entire contents of the baking tray. Add stock, basil, and vinegar; blend until smooth. Season to taste. Serve either hot or cold.
