Season 2 chicken thighs with salt and pepper. Heat 2 tbsp olive oil in a soup pot over medium-high and brown the chicken well on both sides. Remove and set aside (it doesn’t need to be cooked through). Lower the heat to medium. Add diced shallot and a pinch of salt; cook until soft. Add 6 ounces of sliced mushrooms and cook until they release moisture and start to brown. Once mushrooms are soft, stir in 2 cloves minced garlic along with the zest of 1 lemon. Cook for another minute or two, until garlic is fragrant.
Return chicken thighs to the pot. Add 6 cups of chicken stock and bring to a gentle simmer. Cook 10-15 minutes until chicken is cooked through and tender. Pull out the chicken, shred the meat using two forks, then return the shredded chicken to the pot. Add orzo and simmer until orzo is al dente. While simmering, whisk 2 eggs together with the juice of 1 lemon. Whisk very thoroughly.
Carefully and slowly whisk in about 1/4 cup of the hot chicken broth from the pot. This will temper the eggs so they don’t curdle in the soup. You can use more or less broth with the eggs, just so long as the egg-lemon mixture is warm when you add it into the soup.
Turn off the heat. While stirring gently, pour in the egg-lemon-broth mixture. Once fully incorporated, taste and add more salt and pepper as needed. Mix in 2-4 tbsp chopped dill. Serve hot and garnish with more fresh dill, another squeeze of lemon, and more black pepper.