Preheat oven to 400 degrees F. Slice potatoes, and then cut slices into fourths. In a separate bowl, whisk together cream, milk, flour, minced garlic, salt, and plenty of freshly ground black pepper.
Smear softened butter all over the bottom of a baking dish. 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. Allow to stand for a few minutes before serving by the spoonful. Delicious!