Heat olive oil in a large pot over medium heat. Add the diced onion and cook for about 5 minutes, stirring occasionally, until softened. Add the minced garlic and saut? for another 1-2 minutes, just until fragrant.

Pour in the chicken broth and bring it to a boil. Add the rice and reduce to a simmer. Cook for 10-12 minutes, or until the rice is tender.

While the rice cooks, whisk the eggs in a medium bowl until frothy. Slowly add the lemon juice, whisking constantly to combine.

Gradually ladle 1-2 cups of hot broth into the egg-lemon mixture, whisking continuously. Once tempered, slowly pour the mixture back into the pot, stirring as you go.

Stir in the shredded chicken and let it heat through, about 5 minutes. Be careful not to boil the soup after adding the egg mixture?it can cause the creamy texture to separate. Season with salt and pepper to taste.

Ladle the soup into bowls, top with a sprinkle of fresh dill, and serve with lemon wedges on the side.