Preheat the oven to 350°F.
Sauté the onion with the beef in a skillet until cooked through.
Layer some of the potatoes in a greased 13 x 9-inch baking dish.
Grind over some salt and pepper.
Add ⅓ of the meat mixture on top.
Add ⅓ of the cheese.
Repeat the layers twice more, finishing with the remaining cheese.
Mix the cheese soup mix with both milks, adding a little salt and black pepper if needed.
Pour this over the beef and potatoes mixture.
Cover the baking dish with foil and bake for 1 hour.
Discard the foil and bake for another 15 minutes or until the potatoes are tender.