Add the oil, butter, and onion to a pot over medium-high heat. Sauté the onion for 3-4 minutes.
Add the garlic, Italian seasoning, and orzo. Cook for 2-3 minutes, stirring often (this infuses the orzo with more flavor and toasts it a little).
Stir in the chicken broth, lemon juice, and cream. Once it starts to bubble, continue cooking for 10 minutes, uncovered, stirring fairly often. You will probably need to turn the heat down a bit (to medium or even medium-low). It should gently bubble vs. furiously boil, and you don't want the liquid to reduce too much before the pasta has cooked. See notes below and blog post for troubleshooting tips.
Stir in the chicken.
Take the pot off the heat, stir in the parmesan and spinach, and cover the pot for 3-5 minutes or until it has thickened up to your liking. Season with salt & pepper as needed and serve immediately.
Notes
Serves 4-6 depending on how much people eat.
I don't recommend subbing the cream. There's a good chance the sauce will curdle with something lower fat (due to the fairly high heat + citrus).
If the pasta is soaking up the liquid too fast (like before the orzo is cooked), turn the heat down and/or add a splash more broth or cream. If there's too much liquid, cover the pot for longer than suggested in the recipe and the orzo will absorb it quickly.
Orzo is pasta. If you want to make this with rice, you may have to adjust liquid measurements and cooking time (it's a different recipe that I have not tested).