Place the broth, water and brown rice in a large pot over high heat. As soon as it is boiling, reduce the heat to medium and simmer for about 30 minutes until the rice is just starting to become tender.

Taste. Add salt and pepper as needed.

Add the carrots & celery and simmer for another 10 minutes until these are tender. Turn off the heat.

Taste again and add more salt & pepper if it is still needed.

Juice the lemon and whisk together with the eggs in a medium sized glass bowl. Scoop out about a 1/4 cup of broth. Drizzle into the lemon-eggs while whisking rapidly. Add more broth, while whisking. Repeat until the eggs feel warm to the touch.

Turn heat back on to low.

Now, whisk the soup and slowly beat in the tempered and warmed eggs. Beat over low heat until the soup appears creamy and smooth.

Garnish with a sprig of fresh herbs or chives.

Please note
If you add the eggs while they are still cold, this will be more like an egg drop soup. Edible, but the eggs may curdle and cook rather than thicken the soup. The soup is still edible and probably tasty, albeit different from an Avgolemono.

Leftovers are a bit challenging with this soup. Basically, when this soup is reheated the eggs will curdle and cook. It may be what you enjoy. If you want to have leftovers, reserve half of the egg & lemon mixture and soup mixture in separate containers. To heat the next day, warm the soup and temper the eggs by whisking the hot broth into the cold eggs. Repeat the rest of the recipe as if you are making it for the first time.