Preheat and prep: Heat the oven to 375°F (190°C). Lightly spray a 9x13-inch baking dish with olive oil spray.
Cook the pasta: Boil pasta in salted water until just shy of al dente (1–2 minutes less than package). Drain and set aside.
This prevents mushy noodles later.
Cook the chicken: Heat 1 tablespoon olive oil in a large skillet over medium-high heat. Add chicken, season with a pinch of salt and pepper, and cook until just cooked through and lightly browned, 5–7 minutes. Transfer to a plate.
Sauté aromatics: In the same pan, add onion and cook 3–4 minutes until softened.
Stir in minced garlic and cook 30 seconds until fragrant.
Build the sauce base: Pour in chicken broth and milk. Bring to a gentle simmer over medium heat.
Thicken the sauce: Stir the cornstarch slurry to recombine, then whisk it into the simmering liquid. Cook 2–3 minutes, whisking, until the sauce lightly thickens.
Add flavor and protein: Reduce heat to low.
Whisk in Parmesan, salt, black pepper, garlic powder, and red pepper flakes. Turn off the heat, then whisk in Greek yogurt until smooth and creamy. Do not boil after adding yogurt.
Combine: Add the cooked chicken, pasta, and broccoli to the sauce.
Toss gently to coat everything evenly.
Assemble the bake: Transfer the mixture to the prepared baking dish. Sprinkle mozzarella and a little extra Parmesan on top.
Bake: Bake uncovered for 15–18 minutes, until the top is melted and the edges are bubbling. If you want a golden top, broil for 1–2 minutes at the end.
Rest and garnish: Let it rest for 5 minutes so the sauce sets slightly.
Sprinkle with chopped parsley and serve warm.