Heat the oven to 350°F (175°C) and grease a 2½- to 3-quart casserole dish. Peel the potatoes and slice them uniformly, about 1/8 inch thick, so they soften evenly.

Brown the ground beef and chopped onion in a skillet over medium heat until the beef is fully cooked and the onion is tender. Drain off excess fat, then set the beef mixture aside.

Whisk together the condensed cream of mushroom soup, milk, and undrained chopped green chiles in a bowl. Stir until the mixture is smooth and evenly combined.

Arrange a layer of sliced potatoes in the prepared casserole dish, followed by part of the beef and onion mixture. Season lightly with salt and black pepper, then repeat the layers until the ingredients are used.

Pour the soup mixture evenly over the layered potatoes and beef. Cover the casserole tightly with foil so steam remains inside during the main baking period.

Bake the covered casserole for about 1 hour, checking the potatoes with a thin knife near the center. If the slices are not yet tender, continue covered baking until they can be pierced easily.

Remove the foil and sprinkle the shredded cheddar cheese evenly over the top. Return the casserole to the oven and bake for another 15 to 20 minutes, until the cheese has melted and is lightly browned.

Let the casserole rest for 5 to 10 minutes before serving. This brief rest allows the creamy sauce to settle and makes the layers easier to spoon onto plates.