(Optional step) Caramelise the onion. Saute the one chopped onion with 2 tablespoons of olive oil for around 20min. This step is not necessary, but the caramelised onion will add some more flavour to the soup. Leave on the side.
In a large bowl, mix together the minced meat, rice, grated onion, chopped (or caramelised) onion, egg, 2 tablespoons of olive oil, parsley, mint, salt and pepper.
Roll the mince mixture into meatball size portions and coat with the tapioca or cornflour.
(Optional step) place butter and the last 2 tablespoons of olive oil in the same pot you sauteed the onion in. Place the meatballs in batches and shallow fry in medium-high heat until they start to get some colour on all sides. You don't want to cook them through. Remove them from the pan and leave them on the side.
Place the stock into a large deep pot and bring it to a boil. Carefully place meatballs into the cooking pot, one by one. Bring back into a boil and cook on medium heat for around 30min.
When the youvarlakia soup has cooked, switch it off, cover and leave on the side to prepare the avgolemono sauce.
Prepare the avgolemono sauce. Using a handheld mixer or blender, beat the egg whites with 2 tablespoons of water on high for around 2 minutes, until fluffy. Add the 3 egg yolks and continue beating on high for another minute. Then add the lemon juice and zest and continue mixing for another 30sec. Reduce the speed to medium-low and with a ladle spoon, start adding liquid from the pot to the mixer in a SLOW STREAM. It is very important to pour the liquid very slowly at the start, as this will temper the egg mixture gently and prevent it from curdling. Continue adding the stock, gradually increasing the amount as the mixture warms up and is less likely to curdle.
When you have added 4-5 ladlefuls of liquid into the egg mixture, pour the avgolemono sauce back into the pot (that has been removed from the heat) while stirring continuously in a circular motion for a few seconds until well combined. Because we switched off the pot of soup a few minutes ago, the soup is still very hot; therefore, once you add the avgolemono sauce in, it will start to thicken the meatball soup and cook the egg without needing to be over the heat. If you need to warm up the soup, you can heat it up slowly over low heat after adding the avgolemono sauce, but do not let it boil as the soup may curdle.
Serve hot and enjoy!