Place the chicken thighs, cold water, quartered onion, peppercorns, and kosher salt in a large pot. Bring to a gentle boil over medium-high heat, then reduce to a simmer. Skim any foam from the surface. Simmer gently for 35 to 40 minutes until the chicken is cooked through and the broth smells rich.

Remove the chicken thighs and set on a plate to cool slightly. Strain the broth through a fine mesh sieve into a clean pot and discard solids. Return the clear broth to medium heat and bring to a simmer.

Add the orzo to the simmering broth and cook 8 to 10 minutes until tender but not mushy. The broth should be gently bubbling and the orzo plump.

While the orzo cooks, make the avgolemono emulsion. In a medium bowl, whisk together the eggs and the 1/4 cup lemon juice until pale and frothy. Temper the eggs by ladling about 1 cup of the hot broth into the egg mixture in a slow steady stream while whisking vigorously. The mixture should become warm and slightly thickened and glossy.

Reduce the heat to low. Slowly whisk the tempered egg-lemon mixture into the pot of soup. Do not boil the soup after adding the eggs because boiling will cause curdling; the soup should be steaming and slightly thickened. Taste and adjust salt and lemon if needed.

Shred the chicken meat off the bones and discard bones and skin, or chop to bite-size pieces. Stir the shredded chicken back into the soup, warm through for 1 to 2 minutes, and finish with thin lemon slices, a few sprigs of dill or oregano, and freshly ground black pepper.