Heat the oil and butter in a large skillet or saucepan big enough for the sauce and pasta. Make sure it doesn't burn.
Add the onion and sauté for about two minutes until the onion is transparent. Then, add the garlic and sauté for 1 minute
Add the orzo and mix well until combined. Add salt and pepper to taste and stir for about one minute.
Stir in the broth, milk, and other seasonings. Mix well. Bring to a boil and cook for about 8 minutes or until the pasta is al dente. You will notice most of the liquid is absorbed. If you see it is too thick, you can add a half cup of extra chicken broth.
In a separate pan, heat the whipping cream until it is warm, but not boiling.
Add whipping cream to pasta and stir until combined. Then, add the spinach and Parmesan cheese. Mix well until combined but be careful not to break the pasta.
Taste and season with salt and pepper if needed.
Serve immediately and garnish with additional Parmesan cheese.