Mix the mince with 1 egg, two-thirds of the rice, salt and pepper and shape into ping-pong ball-sized meatballs; roll them in flour.
In a large pot, soften the onion in the fat, pour in 2 litres of water and bring to the boil.
Drop the meatballs one by one into the boiling water and cook for 25 minutes; then add the remaining rice, cook for another 15 minutes and take off the heat.
In a bowl, whisk the egg white with a little water until frothy, add the lemon juice, then whisk in the yolk (this is avgolemono).
Whisking constantly, slowly pour in 250 ml of hot soup, then pour it all back into the pot and serve hot.