Step 1

Preheat the oven to 350 degrees F. Grease a 9-by-13-inch baking dish with 1 tablespoon of the butter.

Step 2

Melt the remaining 4 tablespoons butter in a large saucepan over medium-high heat. Add the garlic powder, onion, 1/2 teaspoon salt and a few grinds of pepper and cook until the onion is softened, about 5 minutes. Add the flour and cook, whisking, until sizzling all over and light golden, about 2 minutes. Whisk in the half-and-half and chicken broth, return to a simmer and cook until thickened, about 1 minute. Remove from the heat and stir in the sour cream and 1 1/2 cups of the Cheddar. Add the hash browns and toss until coated in the sauce. Add salt and pepper to taste.

Step 3

Transfer the hash brown mixture to the prepared baking dish, then top with the remaining 1/2 cup Cheddar. Bake until browned and bubbling at the edges, about 45 minutes. Raise the oven temperature to 475 degrees F and continue to bake until the top is crisp and browned all over, about 5 minutes.