Put the garlic, egg yolk and bread in a blender or food processor. With the motor running, slowly add the oil in a thin steady stream until the mixture turns to mayonnaise.
Add the chopped tomatoes, onion, cucumber, peppers and tomato purée in batches, and continue blending until smooth.
Season with salt and pepper to taste, and chill in the refrigerator until ready to serve.
Just before serving, check the seasoning and adjust if necessary. Serve cold with lemon wedges for squeezing over.