Prep the base. Add onion, carrots, celery, garlic, oregano, thyme, bay leaf, and a drizzle of olive oil to the slow cooker.
If you like, lightly sauté the veggies in a pan first for extra flavor, but it’s optional.
Pour in the broth. Add the chicken or vegetable broth. If using a Parmesan rind, toss it in now.
Slow cook. Cover and cook on Low for 5–6 hours or on High for 2–3 hours, until the vegetables are tender.
Add the orzo. Stir in the orzo and cook for another 20–30 minutes on High, until the pasta is tender but not mushy. Stir once or twice to prevent sticking.
Finish with greens and lemon. Remove the bay leaf (and Parmesan rind).
Stir in the spinach or kale, letting it wilt for 2–3 minutes. Add lemon zest and juice. Start with the zest and juice of one lemon, then add more to taste.
Season and serve. Add salt, pepper, and red pepper flakes if you like.
Stir in chicken now if using, just to warm through. Ladle into bowls and top with fresh parsley or dill. A sprinkle of grated Parmesan is a nice touch.