Preheat oven to 400°.
Smear softened butter all over the bottom of a baking dish.
Slice potatoes, then cut slices into fourths.
Whisk together cream, milk, flour, minced garlic, salt, and plenty of freshly ground black pepper in a separate bowl.
Place a third of the potatoes in the bottom of the baking dish. Pour a third of the cream mixture over the potatoes.
Repeat this two more times, ending with the cream mixture. Cover with foil and bake for 30 minutes. Remove foil and bake for 20 minutes, or until potatoes are golden brown and really bubbling. Add grated cheese to the top of the potatoes and bake for 3 to 5 more minutes, until cheese is melted and bubbly.
Allow to stand for a few minutes before serving by the spoonful. Delicious!