Sauté the aromatics: Warm olive oil in a large pot over medium heat. Add onion, carrot, and celery.
Cook 5–7 minutes until softened. Stir in garlic and cook 30 seconds until fragrant.
Build the broth: Add chicken broth, bay leaf, oregano, thyme, salt, and pepper. Bring to a gentle boil, then reduce to a simmer for 10 minutes to meld flavors.
Cook the orzo separately: In a small pot, boil salted water.
Cook orzo 1 minute less than package directions. Drain and drizzle with a little olive oil to prevent sticking. This keeps the main soup from getting cloudy or gummy.
Add the chicken: Stir the shredded chicken into the soup and simmer 3–4 minutes to warm through.
Brighten with lemon: Turn off the heat.
Stir in lemon zest and juice. Taste and adjust salt, pepper, and lemon to your liking. You want a clean, bright finish.
Fold in greens and herbs: Add spinach (if using) and let it wilt in the residual heat.
Stir in chopped dill or parsley. For a silkier mouthfeel, stir in butter until melted.
Serve: Spoon a portion of orzo into each bowl, ladle soup over the top, and garnish with extra herbs. Add a lemon wedge on the side for an extra squeeze.