1. In a large pot, heat the olive oil over medium heat. Add the chopped onion and sauté until translucent and fragrant, about 4-5 minutes. Stir in the minced garlic and dried oregano, cooking for another minute until aromatic.
2. Pour in the chicken broth and bring it to a simmer. Add the rice, cover, and let it cook gently for about 15-18 minutes, or until the rice is tender but not mushy. Stir occasionally to prevent sticking.
3. While the rice cooks, whisk together the eggs and fresh lemon juice in a medium bowl until smooth. This mixture is the magic that gives the soup its creamy texture.
4. Once the rice is cooked, remove the pot from heat. Slowly ladle about one cup of the hot broth into the egg-lemon mixture, whisking constantly to temper the eggs and avoid curdling.
5. Gradually pour the tempered egg-lemon mixture back into the pot, stirring gently to combine. Return the pot to low heat and warm the soup without boiling for 2-3 minutes until it thickens slightly. Stir continuously—this step is key to achieving that silky, velvety texture.
6. Add the shredded cooked chicken to the soup and season with salt and freshly ground black pepper to taste. Heat through for another 2-3 minutes, allowing the flavors to meld.
7. Remove from heat, garnish with fresh parsley, and serve immediately.

My biggest tip here is patience with the tempering step. When I first started, I was so eager to get the soup on the table that I rushed it—and ended up with scrambled eggs in my broth. Tempering the eggs slowly is the trick I learned standing on that kitchen stool, and it makes all the difference.