Preheat oven to 400 degrees.
Smear softened butter all over the bottom of a baking dish.
Slice potatoes, then cut slices into fourths.
In a separate bowl, whisk together cream, milk, flour, minced garlic, salt, and plenty of freshly ground black pepper.
Place 1/3 of the potatoes in the bottom of the baking dish. Pour 1/3 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.
(I HAVE FOUND THAT THESE COOKING TIMES ARE NOT LONG ENOUGH. I COOK THEM AT 300 FOR 2 HOURS INSTEAD AND THEY TURN OUT MUCH MORE TENDER. I STILL REMOVE THE FOIL FOR THE LAST 20 MINUTES OR SO AND ADD THE CHEESE RIGHT AT THE END)
Allow to stand for a few minutes before serving by the spoonful. Delicious!
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