Sauté the aromatics: Add the olive oil, butter, and chopped onion to a large pot over medium-high heat. Sauté the onion for 3-4 minutes until it becomes translucent and softened.
Toast the orzo: Add the minced garlic, Italian seasoning, and uncooked orzo to the pot. Cook for 2-3 minutes, stirring often. This step infuses the orzo with more flavor and toasts it slightly, adding a subtle nutty depth to the finished dish.
Add the liquids: Stir in the chicken broth, lemon juice, and heavy cream. Once the mixture starts to bubble, continue cooking for 10 minutes, uncovered, stirring fairly often. You'll probably need to turn the heat down a bit to medium or even medium-low. The liquid should gently bubble rather than furiously boil—you don't want it to reduce too much before the pasta has finished cooking.
Add the chicken: Stir in the shredded cooked chicken, making sure it's distributed throughout the orzo.
Finish with cheese and spinach: Take the pot off the heat and stir in the freshly grated Parmesan cheese and fresh baby spinach. Cover the pot for 3-5 minutes, or until the mixture has thickened to your liking. The spinach will wilt beautifully in the residual
Season and serve: Taste and season with salt and pepper as needed. Serve immediately while hot and creamy.