Warm the pot: Heat olive oil in a large pot over medium. Add onion and a pinch of salt.
Cook 3–4 minutes until translucent. Stir in garlic for 30 seconds.
Add broth and simmer: Pour in chicken broth. Add turmeric if using.
Bring to a gentle simmer.
Cook the starch: Stir in orzo and cook until al dente, about 7–9 minutes. If using cooked rice, add it later with the chicken.
Prep the lemon-egg mix: In a bowl, whisk eggs until frothy, 30–45 seconds. Whisk in lemon zest and juice slowly.
Temper the eggs: Ladle 1 cup of hot broth into the egg-lemon mixture, whisking constantly to prevent curdling.
Repeat with another 1/2–1 cup.
Finish the soup: Lower the heat to low. Slowly stir the tempered egg mixture into the pot. Add shredded chicken (and cooked rice if using).
Warm gently 2–3 minutes. Do not boil.
Season and serve: Taste and season with salt and pepper. Add more lemon if you like it brighter.
Garnish with chopped dill or parsley.