Recipe from The New Complete International Jewish Cookbook, Pavilion 

• Have ready a large soup pan. Trim the beets, wash thoroughly and peel only if they are old. Peel the onion and the carrot. Cut all the vegetables into roughly 2.5 cm (1 inch) chunks, then chop in the food processor in two batches until very finely chopped.
• Put the vegetables in the pan, with the water, stock cubes, pepper, salt and sugar or sweetener.
• Bring to the boil, cover and simmer for 20 minutes, until the vegetables are soft and the liquid is a rich, dark red.
• Pour the contents through a coarse strainer into a bowl and discard the vegetables. Return the strained beet juice to the pan and leave on a low heat.
• Put the lemon juice and the whole eggs into the food processor and process for 5 seconds until well mixed. With the motor running, pour two ladles of the hot beet juice through the feed tube and process for a further three seconds, then add the mixture to the beet juice in the pan and heat gently, whisking constantly with a batter whisk or balloon whisk until the soup is steaming and has thickened slightly. Do not let it boil or it will curdle. Taste and adjust the seasoning so that there is a gentle blend of sweet and sour.
• Chill thoroughly. Just before serving, whisk in the soured cream, yoghurt or fromage frais.
• Fill large wineglasses one-third full with ice cubes and fill up with the chilled borscht.