Sauté the base: Warm 2 tablespoons of olive oil in a large pot over medium heat. Add the onion, carrots, and celery with a pinch of salt.
Cook 6–8 minutes until the vegetables soften and the onion turns translucent.
Add aromatics: Stir in the garlic, tomato paste, oregano, thyme, and red pepper flakes. Cook 1 minute, stirring, until fragrant. This step builds flavor, so don’t skip it.
Deglaze and simmer: Pour in the chicken broth, scraping up any browned bits.
Add the bay leaf and Parmesan rind if using. Bring to a gentle boil, then reduce to a simmer.
Cook the orzo: Stir in the orzo and simmer 8–10 minutes, stirring occasionally so it doesn’t stick. Taste the broth and adjust salt as needed.
Add chicken and greens: Stir in the shredded chicken and kale or spinach. Simmer 2–3 minutes, just until the greens wilt and the chicken is heated through.
Finish with brightness: Turn off the heat.
Stir in the lemon zest, then add lemon juice to taste. Fold in the chopped parsley or basil. Season with pepper, and more salt if needed.
Serve: Ladle into bowls and top with grated Parmesan if you like. Add a drizzle of olive oil for extra richness.