In a large pot, heat the olive oil over medium heat. Add the chopped onion, garlic, carrot, and celery. Sauté for about 5-7 minutes until the vegetables are softened and the onion is translucent.
Pour in the vegetable broth and bring to a gentle boil.
Once boiling, add the cooked rice to the pot. Reduce the heat to medium-low and let it simmer for about 10 minutes.
In a separate bowl, whisk together the eggs, lemon juice, and lemon zest until smooth.
Gradually whisk a ladleful of the hot soup into the egg and lemon mixture to temper it, then slowly stir the tempered mixture back into the soup pot. This will create a creamy texture without curdling the eggs.
Cook the soup on low heat for an additional 5 minutes, stirring gently. Do not let it boil at this stage.
Season with salt and pepper to taste.
Serve the soup hot, garnished with fresh dill or parsley for a pop of color and flavor.
Notes
For a richer flavor, use homemade vegetable broth.