Prepare the Meatball Mixture:
In a large bowl, combine all the ingredients for the meatballs. Mix thoroughly and knead well to ensure the rice is evenly distributed throughout the meat mixture. Cover and refrigerate for about 30 minutes to allow the rice to swell slightly.

Make the Sauce Base:
In a large pot, melt the butter over medium heat. Add the flour and stir with a whisk for 2-3 minutes, until the mixture is well combined and lightly cooked.

Add Broth:
Remove the pot from the heat and slowly pour in the hot broth, whisking constantly to avoid lumps. Return the pot to the heat and bring the sauce to a gentle boil, stirring frequently.

Form the Meatballs:
While the sauce is heating, shape the meat mixture into small, round meatballs. Drop the meatballs gently into the simmering sauce, and let them cook on low heat for about 20 minutes.

Prepare the Avgolemono (Egg-Lemon Sauce):
In a separate bowl, whisk the eggs with the lemon juice. Gradually add a bit of the hot sauce to the egg mixture, stirring constantly to avoid cooking the eggs. Once the eggs are tempered, slowly pour the mixture back into the pot, stirring gently.

Finish Cooking:
Allow the soup to simmer on low heat for a few more minutes until the sauce thickens and the meatballs are fully cooked. Remove the pot from the heat and let it cool slightly before serving.

Serve and Enjoy:
Serve the Yuvarlakia hot, garnished with a dollop of Greek yogurt for added creaminess.