This soup is light, yet hearty, making it perfect for the ever-changing weather of spring. Escarole is an often over-looked green, but it's always available and is very forgiving, easy to cook and adds a slight note of bitterness to this otherwise mild dish.
Heat the olive oil in a large pot or Dutch oven over medium heat. Add the leeks and carrots and cook until just beginning to soften, 1 to 2 minutes. Add the chicken broth, chicken thighs and barley. Cover the pot, increase the heat to high and bring to a rapid simmer. Uncover, reduce the heat to medium and simmer until the chicken is cooked through, about 16 minutes.
Remove the chicken to a bowl. Add the escarole to the pot. Shred the chicken with two forks and return to the pot. Simmer until the barley is tender, about 12 more minutes.
Whisk the eggs in a medium bowl. Whisk in the Parmesan, 1/4 teaspoon salt and a few grinds of pepper. Stir the soup slowly in a clockwise direction and slowly drizzle in the egg mixture. Once you’ve added all the egg, remove the soup from the heat; season with salt and pepper. Stir in the lemon juice and parsley.