In a large pot, bring 6 cups of low-sodium chicken broth to a rolling boil over medium-high heat. Once boiling, add 1 cup of medium-grain white rice, reduce the heat to a simmer, and cover the pot. Cook for 15-20 minutes, or until the rice is tender and has absorbed most of the broth, stirring occasionally to prevent sticking.

While the rice cooks, separate 3 large eggs, placing the whites in one bowl and the yolks in another. Using a whisk or electric mixer, beat the egg whites until they are frothy and form soft peaks, which should take about 2 minutes. Next, gently whisk in the egg yolks until the mixture becomes pale and creamy.

Once the rice is cooked, begin tempering the egg mixture to avoid curdling. Gradually ladle about ½ cup of the hot broth into the egg yolk mixture while whisking continuously.

Remove the pot from heat after cooking the rice, allowing it to cool slightly. Slowly pour the tempered egg mixture back into the pot while stirring continuously for about one minute.

Stir in the zest of one lemon and ¼ cup of fresh-squeezed lemon juice into the soup. Season with salt and freshly ground black pepper to taste, adjusting according to the broth's saltiness.

Ladle the warm Greek Egg and Lemon Soup into bowls, and garnish each serving with a sprinkle of fresh dill or parsley. Serve immediately.