Grease the bottom and sides of a baking dish with the softened butter.
Wash and scrub the potatoes clean but don't worry about peeling them. Slice the potatoes into thick slices (somewhere between 1/4 and 1/2 inch thick), then stack the slices and cut them into 4 pieces. Put all of the potato pieces in the bottom of the baking dish.
In a small bowl whisk the cream, milk, flour, garlic, salt, and pepper together. Pour the mixture over the potatoes.
Cover the dish with foil and bake for 40 minutes. Remove the foil and bake for another 10 minutes.
Add the cheese to the hot dish and bake for another 3-5 minutes until the cheese is all melted. Serve hot.
Notes
To make this recipe gluten-free, switch out the 2 tablespoons of flour with 1 tablespoon of corn starch.
Use a mandolin or food processor to quickly and easily slice the potatoes.
Heavy cream in place of the milk will give you a richer, creamier sauce.
Keep any leftovers in an air-tight container in the fridge.