Preheat the oven to 350°F. Grease a 10-inch square baking dish with butter or cooking spray. Place the potatoes in a large pot and cover with water. Bring to a boil and cook until fork tender, about 10-15 minutes. Drain the potatoes and transfer them back to the hot pot.

While the potatoes are boiling, steam or roast the broccoli until hot and barely softened. It should still be a little bit crisp. Drain any liquid from the broccoli. Cook the bacon, chop or crumble and set aside.

Place the pot with the potatoes back over the warm (but turned off) burner. Smash the potatoes with a potato masher. Add the butter, sour cream, salt, pepper, garlic, and paprika. Stir to combine.

Add the cooked broccoli, chicken, bacon, and 1 cup of cheese to the pot. Stir to mix throughout and then transfer to the prepared baking dish. Sprinkle with the remaining cheese. Bake for 20-25 minutes, until the cheese has melted and the casserole is heated through.