Dice the onion, mince the garlic, cut the chicken into bite-size pieces, and chop the broccoli into very small pieces; set all ingredients out so you can work quickly.
Heat the olive oil in a large nonstick pot over high heat. Add the diced onion and cook for about 2 minutes until softened.
Add the minced garlic and cook, stirring, for 30 seconds until fragrant.
Add the chicken, season with salt and pepper, and cook for about 5 minutes until mostly cooked through.
Add the frozen diced vegetables and chopped broccoli to the pot and stir for 2–3 minutes until the frozen vegetables are thawed and the broccoli is crisp-tender; transfer the mixture to a plate and cover to keep warm.
Reduce heat to medium and melt the butter in the same pot. Whisk in the flour and cook, whisking constantly, for 1 minute to make a roux.
Gradually whisk in the chicken stock until smooth, then add the milk and uncooked orzo. Stir in the Italian seasoning.
Bring the mixture to a simmer, then reduce 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 and stir to combine. Add 3/4 cup of the grated Parmesan a handful at a time, stirring until melted and incorporated. Taste and adjust salt and pepper as needed.
Serve the orzo hot with the remaining Parmesan sprinkled on top and fresh parsley if desired. Add a splash of milk if you prefer a thinner consistency.