Grate the onions and carrots on a coarse grater. Saute them in the oil with a little water to soften them. Add the diced potatoes (peeled and washed beforehand) , add water (6 1/5 cups (1.5 L)). Allow the water to come to a boil, then add the meatballs.
Make the meatballs as follows: mix the minced meat with the rice, egg white and spices. Mix everything and make small balls, roll them in flour and place in the boiling water. Add the tomato paste and allow the soup to boil for 15-20 minutes. Then add the vermicelli and spices. Let it boil for 10-15 minutes until the vermicelli is fully cooked. If necessary, add more water if the soup is too thick.
For the thickening agent: combine the yoghurt with the egg yolk and vinegar and mix well. Remove the finished soup from the heat, add 4-5 ladles of broth to the thickening agent and stir well (this is done to equalize the temperatures of the thickening agent and soup). Then add it to the soup while stirring.
Return the soup to the heat and simmer for 2-3 minutes, while stirring.