Dice the onion, mince the garlic, cut the chicken into bite-size pieces, and chop the broccoli into very small pieces; have other ingredients measured and ready.
Heat the olive oil in a large nonstick pot over medium-high heat. Add the diced onion and cook about 2 minutes until softened.
Stir in the minced garlic and cook 30 seconds, then add the chicken pieces. Season with salt and pepper and cook about 5 minutes until mostly cooked through.
Add the frozen diced vegetables and chopped broccoli to the pot and stir 2–3 minutes until vegetables are thawed and broccoli is crisp-tender. Transfer the chicken and vegetables to a plate and cover to keep warm.
In the same pot, melt the butter over medium heat. Sprinkle the flour over the butter and whisk constantly for 1 minute to form a roux.
Gradually whisk in the chicken stock, then add the milk and the uncooked orzo. Stir in the Italian seasoning.
Bring the mixture to a simmer, then reduce the heat to maintain a gentle simmer. Cook uncovered for about 7 minutes, stirring often to prevent sticking; the mixture will be slightly soupy.
Return the cooked chicken and vegetables to the pot. Stir in 3/4 cup of the grated Parmesan a handful at a time until melted and incorporated. Taste and adjust salt and pepper if needed.
If the consistency is too thick, add a splash of milk to loosen. Serve hot topped with the remaining Parmesan and chopped fresh parsley, if using.
