Dice the onion, mince the garlic, cut the chicken into bite-size pieces, and chop the broccoli into very small pieces; have the remaining ingredients ready because cooking moves quickly.
Heat the olive oil in a large nonstick pot over high heat. Add the diced onion and cook for about 2 minutes until beginning to soften.
Stir in the minced garlic and cook for 30 seconds, then add the chicken pieces. 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; stir for 2–3 minutes until the frozen vegetables are thawed and the broccoli is crisp-tender. Transfer the chicken and vegetables to a plate and cover to keep warm.
Reduce heat to medium and melt the butter in the same pot. Sprinkle the flour over the butter and whisk constantly for 1 minute to cook the flour.
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 lower the heat so it gently bubbles. Cook uncovered for about 7 minutes, stirring often to prevent sticking; the mixture will be slightly soupy.
Return the reserved 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.
The finished consistency should be creamy, similar to risotto; add a splash of milk if you prefer it thinner. Serve hot topped with the remaining Parmesan and optional fresh parsley.