1. Prepare the Meatball Mixture: In a large bowl, combine the ground meat, rice, onion, parsley, salt, pepper, 1 tablespoon of high-quality olive oil, and garlic if using. Mix well until all ingredients are evenly distributed.
2. Shape the Meatballs: Form the mixture into small meatballs, about the size of a walnut. You should get around 20-25 meatballs.
3. Boil the Liquid: In a large pot, bring the water or stock to a boil. Add a pinch of salt if using water.
4. Cook the Meatballs: Gently add the meatballs to the boiling liquid. Reduce the heat to a simmer and cook for about 25-30 minutes, or until the meatballs are cooked through and the rice is tender. Skim any foam that forms on the surface during cooking.
5. Prepare the Avgolemono Sauce: While the meatballs are cooking, beat the eggs with the lemon juice in a medium bowl until well combined.
6. Temper the Sauce: Once the meatballs are done, ladle about 1 cup of the hot broth into the egg-lemon mixture, whisking constantly to temper the eggs and prevent them from curdling.
7. Add the Sauce to the Soup: Slowly pour the tempered sauce back into the pot with the meatballs, stirring gently to incorporate.
8. Thicken the Sauce: Heat the soup over low heat for a few minutes to thicken the sauce, but do not let it boil.
9. Adjust Seasoning: Taste and adjust with salt and more lemon juice if desired.
10. Serve: Serve hot, garnished with additional chopped parsley if you like, and drizzle each serving with a little high-quality olive oil for extra flavor.