Step 1

Cook chicken and make stock. Place the chicken, water, onion, peppercorns, and salt in a 5-quart or larger Dutch oven. Cover and bring to a boil over high heat. Reduce heat to maintain a simmer and simmer until the chicken is cooked through, about 45 minutes to 1 hour. If any white foam forms, use a slotted spoon to skim off and discard.

Step 2

Strain the broth. Transfer the chicken to a cutting board. Strain the stock through a fine-mesh strainer set over a large heatproof bowl and discard the solids. If there is an abundance of fat rendered from the chicken, skim it off it with a spoon or use fat separator. Reserve 2 cups of the stock in a measuring cup. Return the remaining stock to the Dutch oven and keep warm over low heat.

Step 3

Shred the chicken. When the chicken is cool enough to handle, use your hands to shred the meat into bite-sized pieces; set aside. Discard the skin and bones.

Step 4

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

Step 5

Make the avgolemono. Place the eggs in a medium bowl and whisk until lightened in color and frothy, about 2 minutes. While whisking, slowly pour in the lemon juice. While still whisking, temper in the eggs by slowly drizzling the reserved 2 cups of warm stock into the egg-lemon mixture. This warms the eggs just enough so that they do not curdle when added to the hot soup.

Step 6

Thicken the soup. Add the avgolemono back into the pot with the chicken and orzo and stir to combine. Cook until the soup thickens slightly, 3 to 5 minutes, but do not let it come to a boil.

Step 7

Serve the soup. Pour the soup into serving bowls and serve with lemon slices, fresh chopped dill or oregano, and freshly ground black pepper.