Arrange a rack in the middle of the oven and heat the oven to 375°F. Coat a 9x13-inch baking dish with 1 teaspoon room temperature unsalted butter.
Place 1 (10.25) can cream of chicken or cream of cheddar soup, 16 ounces sour cream, and 1 large egg in a large bowl and whisk until smooth.
Add 32 ounces thawed hash browns, ½ large grated yellow onion, and half of the grated cheddar cheese (about 1 cup) and stir until well combined.
Pour the hash brown mixture into the baking dish and smooth into an even layer. Sprinkle with the remaining grated cheddar cheese (about 1 cup).
Bake until the edges are crisp and the top is beginning to brown, about 45 minutes.
Remove the casserole from the oven and let cool for 10 minutes. Sprinkle with ¼ teaspoon ground black pepper, cut into squares, and serve hot.
