Sauté the aromatics. Warm 1–2 tablespoons olive oil in a large pot over medium heat. Add onion, celery, and carrots with a pinch of salt.
Cook 5–7 minutes, stirring, until softened and lightly golden.
Add garlic and bloom. Stir in garlic (and a pinch of red pepper flakes if using). Cook 30–60 seconds until fragrant but not browned.
Build the broth. Pour in the chicken broth. Add the bay leaf and Parmesan rind if you have them.
Bring to a gentle boil, then reduce to a lively simmer.
Cook the orzo. Stir in the orzo. Simmer 7–9 minutes, stirring occasionally so it doesn’t stick, until al dente. Taste the broth and season with salt and pepper.
Add the chicken. Stir in the shredded chicken and simmer 2–3 minutes to warm through.
Remove the bay leaf and Parmesan rind.
Finish with lemon and herbs. Turn off the heat. Add the zest of 1 lemon and the juice of 1–2 lemons (about 3–4 tablespoons). Stir in a generous handful of chopped dill or parsley.
Taste and adjust salt, pepper, and lemon.
Rest briefly. Let the pot sit 3–5 minutes so flavors settle and the orzo finishes hydrating.
Serve. Ladle into bowls. Add a drizzle of olive oil, extra herbs, or grated Parmesan if you like. Crack more black pepper on top.