Warm the olive oil and butter together in your pot over medium-high heat. Add the chopped onion and let it cook for three to four minutes, stirring now and then, until it turns soft and slightly golden. This step builds the flavor base for everything that follows.
Stir in the garlic, Italian seasoning, and uncooked orzo. Let it cook for two to three minutes, stirring often so nothing sticks or burns. This little bit of toasting gives the orzo a deeper, nuttier flavor once it simmers in the broth.
Pour in the chicken broth, lemon juice, and heavy cream, then stir everything together. Once it starts to bubble gently, let it cook uncovered for about ten minutes, stirring fairly often so the orzo doesn't stick to the bottom of the pot.
Once the orzo has softened and the liquid has mostly been absorbed, stir in the shredded chicken. This is where the dish starts to smell amazing, and you'll notice the sauce thickening up nicely around the pasta.
Take the pot off the heat completely, then stir in the parmesan and fresh spinach. Cover it and let it sit for three to five minutes so the spinach wilts and the sauce thickens to a creamy consistency. Season with salt and pepper before serving.