Heat the olive oil and butter in a large pot or Dutch oven over medium-high heat until the butter melts.
Add the chopped onion and sauté for 3–4 minutes, until softened and translucent.
Add the minced garlic and Italian seasoning, then stir in the orzo and cook 2–3 minutes, stirring frequently to lightly toast the pasta.
Pour in the chicken broth, lemon juice, and heavy cream; bring to a gentle bubble, then reduce the heat to medium or medium-low so it simmers gently.
Simmer uncovered for about 10 minutes, stirring fairly often, until the orzo is tender and most of the liquid is absorbed; adjust heat as needed so it doesn’t boil vigorously.
Stir in the shredded chicken until heated through.
Remove the pot from the heat, stir in the grated Parmesan and the baby spinach, then cover and let sit 3–5 minutes until the spinach wilts and the sauce thickens to your liking.
Taste and season with salt and pepper as needed, then serve immediately.
