Preheat your oven to 400°F (200°C). If you skip this, you’ll be sad later. Grease a 9×13-inch baking dish with a little oil or nonstick spray.
In a large skillet, heat olive oil over medium-high. Sear the chicken chunks until just golden and mostly cooked through. They’ll finish in the oven, so no soul-crushing overcooking required.
Remove the chicken, then toss in the broccoli (and corn, if using) for a quick sauté—about 2 minutes. You still want a bit of bite; soggy veggies are not a vibe.
In a mixing bowl, whisk together cream cheese, sour cream (or yogurt), milk, garlic, onion powder, paprika, salt, and pepper until smooth and creamy.
Return the chicken to the pan with the veggies. Pour the sauce over everything and give it a quick stir to coat evenly.
Transfer the mixture to the prepared baking dish. Sprinkle the shredded cheese across the top.
Bake for 18–22 minutes, or until the cheese is bubbling and melted and the chicken reaches 165°F (74°C). Let it rest a few minutes before serving.