Preheat the oven to 350°F (175°C). Lightly grease a 9x13-inch or 3-quart baking dish and set aside.
Melt 1/4 cup salted butter in a medium saucepan over medium heat. Add the diced onion and cook, stirring occasionally, until softened and lightly browned, about 5 minutes.
Stir in 1/4 cup all-purpose flour and cook for 2–3 minutes, stirring continuously, until the mixture is smooth and golden. Gradually whisk in 1 cup chicken broth, 1 cup heavy cream, and 1 cup sour cream. Stir until smooth and fully combined. Lower the heat to a simmer and cook for 2–3 minutes, stirring occasionally.
Add 4 ounces diced green chiles, 1 tablespoon garlic powder, 1 teaspoon hot sauce, 1 teaspoon black pepper, and 1 teaspoon salt to the sauce. Stir to combine, then remove from heat.
In a large skillet over medium-high heat, brown 2 pounds ground beef, breaking it into small pieces as it cooks, for about 7–8 minutes. Add 1 teaspoon salt and 1 teaspoon black pepper to the beef and stir to combine. Cook until no pink remains, then drain any excess grease.
Wash and peel 3-4 large russet potatoes. Slice them into 1/4 inch slices. Arrange the potato slices evenly in the bottom of the prepared baking dish.
Spread the cooked ground beef over the potatoes, then pour the prepared sauce evenly over the top. Sprinkle with 2 cups shredded cheddar cheese. Cover loosely with foil.
Bake in the preheated oven for 50 minutes. Remove the foil and bake for an additional 10 minutes, or until the potatoes are tender and the top is golden brown and bubbly. Serve hot.
Notes
Short on time? Use frozen shredded hashbrowns in place of the russet potatoes. You'll need 3 pounds, or 48 ounces.