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 add the dry orzo; cook 2–3 minutes, stirring frequently, to lightly toast the pasta.
Pour in the chicken broth, lemon juice, and heavy cream and bring the mixture to a gentle simmer over medium to medium-low heat.
Cook uncovered for about 10 minutes, stirring fairly often, until the orzo is tender and most of the liquid is absorbed; adjust heat as needed to maintain a gentle bubble.
Stir in the shredded chicken to warm through.
Remove the pot from heat, stir in the grated Parmesan and packed baby spinach, then cover and let sit 3–5 minutes until the spinach wilts and the sauce thickens.
Season with salt and pepper to taste and serve immediately.