Preheat your oven to 375°F (190°C). Lightly grease a 9x13 inch baking dish with cooking spray or butter.
Place the diced potatoes in a large pot of salted water. Bring to a boil and cook for 5-7 minutes until just fork-tender but not falling apart. Add the broccoli florets during the last 60 seconds of boiling to blanch them. Drain well and set aside.
In a medium saucepan, melt the butter over medium heat. Whisk in the flour and cook for 1 minute to remove the raw flour taste.
Gradually pour in the milk while whisking constantly to prevent lumps. Simmer for 3-5 minutes until the sauce thickens.
Remove the sauce from heat. Stir in the garlic powder, onion powder, salt, pepper, sour cream, and 1 1/2 cups of the shredded cheddar cheese until smooth.
In a large bowl (or directly in the baking dish), combine the cooked chicken, drained potatoes, and broccoli. Pour the cheese sauce over the mixture and toss gently to coat evenly.
Transfer the mixture to the prepared baking dish if not already there. Sprinkle the remaining 1/2 cup of cheese and the panko breadcrumbs over the top.
Bake for 20-25 minutes, or until the casserole is bubbly and the top is golden brown. Let cool for 5 minutes before serving.