Heat the oven to 400°F. Butter all 12 wells of a standard metal muffin pan generously with the measured butter.
Slice potatoes 1/16 inch thick with a guarded mandoline or sharp knife. Mix cream, garlic, salt and pepper in a large bowl, then turn the slices through the mixture to coat.
Fill the wells halfway with stacked potato rounds, add half the cheddar evenly and finish with remaining potato slices. Divide all loose cream from the bowl among the wells and scatter remaining cheddar over the stacks.
Cover the pan tightly with foil and bake for 25 minutes. Uncover and bake for 15 to 20 minutes until the edges brown and a knife slips through each stack easily.
Rest for 10 minutes, loosen the sides with a thin spatula and lift out carefully. Serve 2 stacks per person.