Preheat oven to 350°F (175°C) and grease a 10-inch baking dish.
Boil chopped red potatoes in salted water for 10–15 minutes until fork-tender, then drain and return to the pot.
While the potatoes cook, steam or roast broccoli until crisp-tender. Cook bacon in a skillet until crisp, then crumble.
Mash potatoes with butter, sour cream, salt, pepper, garlic powder, and paprika until smooth and creamy.
Fold in broccoli, chicken, crumbled bacon, and half the cheese. Mix well.
Spread mixture into the baking dish, sprinkle with remaining cheese, and bake 20–25 minutes until hot and golden.
Let cool for a few minutes before serving.