Pulse well again into a silky smooth reddish soup. Place a fine sieve over a large pan or bowl and pour in the tomato soup. Stir the soup in the sieve well using a spatula or a spoon until you end up with a coarse pulp.
Stir well. Check the seasoning and add extra vinegar, pepper or salt to taste. Transfer the soup to a glass jug and chill it in the fridge for at least 30 minutes. Then stir the salmorejo soup well and pour it into bowls, deep plates or glasses. Garnish with crumbled hard-boiled egg, chopped Serrano ham and a few drops of olive oil right before serving.