Preheat the oven to 375°F (190°C) and grease a baking dish.
In a pot of salted boiling water, cook the cubed potatoes until fork-tender. Drain and set aside.
In the same pot, steam the broccoli until slightly tender. Drain and set aside.
In a large bowl, mix sour cream (or Greek yogurt), milk, garlic powder, onion powder, salt, and pepper until well combined.
Add the cooked potatoes, diced chicken, broccoli, and 1½ cups of cheddar cheese to the bowl, stirring until evenly coated.
Transfer the mixture to the prepared baking dish and spread evenly.
In a small bowl, mix the breadcrumbs with melted butter, then sprinkle over the casserole. Top with the remaining ½ cup of cheddar cheese.
Bake uncovered for 25–30 minutes, or until the cheese is melted and golden brown.
Let cool slightly before serving. Enjoy!