Score a cross in the base of each tomato. Put in a bowl of boiling water for 10 seconds, then plunge into ice-cold water and peel away the skin from the cross. Cut the tomatoes in half and scoop out the seeds with a teaspoon. Chop the tomato flesh.
Soak the bread in cold water for 5 minutes, then squeeze out any excess liquid. Put the bread in a food processor with the tomatoes, bell pepper, garlic, onion, cucumber, chili, sugar, and red wine vinegar and process until combined and smooth.
With the motor running, add the oil and the mayonnaise if used, to make a smooth, creamy mixture. Season to taste. Refrigerate for at least 2 hours.