Place the chicken thighs, cold water, onion, peppercorns, and salt in a 5-quart or larger Dutch oven. Cover and bring to a boil over high heat. Once boiling, reduce the heat to maintain a simmer. Cook until the chicken is fully cooked through, around 45 minutes to 1 hour. Skim off any foam that forms on the surface.

Transfer the cooked chicken to a cutting board. Strain the stock through a fine-mesh strainer into a large heatproof bowl and discard the solids. If there’s too much fat, skim it off with a spoon or use a fat separator. Reserve 2 cups of the stock for later use. Return the remaining stock to the Dutch oven and keep warm over low heat.

When the chicken is cool enough to handle, shred the meat into bite-sized pieces using your hands. Discard the skin and bones.

Bring the stock back to a boil over medium-high heat. Add the dried orzo and cook until al dente, about 7 to 9 minutes. Stir in the shredded chicken. Reduce the heat to low.

In a medium bowl, whisk the eggs until they are light in color and frothy (about 2 minutes). Slowly whisk in the freshly squeezed lemon juice. Gradually add the reserved 2 cups of warm stock to the egg-lemon mixture while whisking constantly to temper the eggs and prevent them from curdling.

Pour the avgolemono (egg-lemon mixture) back into the pot with the chicken and orzo. Stir everything together and cook over low heat for 3 to 5 minutes, until the soup thickens slightly. Be careful not to let the soup boil.

Ladle the soup into bowls and garnish with thin lemon slices, freshly chopped dill or oregano, and freshly ground black pepper.