In a Dutch oven, combine chicken, cold water, onion, peppercorns, and salt. Bring to a boil, then reduce to a simmer for about 45 minutes to 1 hour.

Transfer chicken to a cutting board and strain the broth into a large bowl, discarding solids. Reserve 2 cups of stock and keep remaining stock warm.

Once cool, shred chicken into bite-sized pieces, discarding skin and bones.

Bring the strained stock back to a boil and add orzo. Cook until al dente, about 7 to 9 minutes, then stir in shredded chicken.

In a bowl, whisk eggs until frothy. Slowly add lemon juice while whisking. Temper the mixture by slowly adding warm stock.

Stir the egg-lemon mixture into the pot and cook for 3 to 5 minutes until slightly thickened. Do not boil.

Serve in bowls, garnished with lemon slices, dill or oregano, and freshly ground black pepper.