Dice the carrot into 1/4-inch pieces, chop the celery and onion into similar-sized pieces, and mince the garlic. Having everything prepped and ready is crucial for this soup since we'll be working quickly once the broth is added. Heat the olive oil in a large pot over medium heat until shimmering, then add the carrots, celery, and onion. Sauté for 5-8 minutes, stirring occasionally, until the vegetables soften and begin to release their aromatics—you're looking for them to become slightly translucent at the edges.

Add the minced garlic to the softened vegetables and stir constantly for about 30 seconds until fragrant—don't let it brown or it will taste bitter. Pour in the oregano and parsley, stirring to coat the vegetables evenly so the dried herbs bloom in the hot oil. This step releases their essential oils and distributes the flavor throughout the soup base. Immediately pour in the chicken broth and increase the heat to bring the liquid to a boil.

Once the broth is boiling, stir in the rice and return to a boil. Cover the pot with a lid and reduce the heat to low, simmering for about 20 minutes until the rice is tender and has absorbed most of the liquid. I like to keep the heat low and steady here—too high and the rice can scorch on the bottom of the pot, which creates an unpleasant flavor.

While the rice cooks, whisk the room-temperature eggs together in a small bowl with the freshly squeezed lemon juice until well combined. Once the rice is tender, remove the pot from heat and let it cool for about 1 minute—this is critical because adding the egg mixture directly to boiling broth will cause it to curdle. Slowly ladle one ladle of the hot broth into the egg-lemon mixture while whisking constantly to gently raise the temperature of the eggs. This tempers the eggs and prevents scrambling.

Slowly pour the tempered egg-lemon mixture back into the pot while stirring gently and constantly—the gentle heat from the soup will cook the eggs, creating a silky, light texture throughout the broth. Add the shredded chicken, salt, and pepper, stirring to distribute evenly. Taste and adjust the seasoning if needed; I find the lemon juice may require a touch more salt depending on how acidic you want the final soup to be. Heat gently over low heat for 1-2 minutes just until warmed through, but do not boil or the eggs will break apart.

Ladle the soup into bowls and top each serving with a sprinkle of fresh parsley for brightness and color. Serve immediately with crackers on the side—I always use Ritz for that buttery crunch that balances the bright, lemony broth perfectly.