Preheat oven to 350°F/180°C (all oven types).
Brush muffin tin with butter: Melt butter in a saucepan over medium heat then use what you need to lightly brush the muffin tin holes with butter. (Remaining butter is for the cream sauce)
Cream sauce: Into the remaining butter, add garlic and cook for 20 seconds. Add cream and salt then bring to a simmer. Simmer for 30 seconds, then remove from stove and keep warm.
Slice potato: Peel potatoes. Trim base so it stands upright. Then cut into cylinder shapes that fit the muffin tin. Cut into 2mm/ 1/10" slices using a mandolin or sharp knife.
Assemble stacks: Place potato slices into the muffin tin so they go halfway up the muffin tin holes. Try to match by size to make them into neat stacks.
Cream: Drizzle each potato stack with 1 tsp of cream mixture – use 1/2 of the mixture.
Cheese slice: Top with cheese slice.
Top with potato, cream then thyme: Top each stack with remaining potato slices so the height is about 1cm / 1/3" above the rim of the muffin tin (they sink once baked). Drizzle with remaining cream mixture and sprinkle with most of the thyme (reserve some for topping).
Baked 40 minutes: Cover loosely with foil and bake for 40 minutes or until potato is cooked through. A small sharp knife should go through without any resistance.
Top with cheese, bake 10 minutes: Remove from oven, sprinkle with shredded cheese and bake without foil for 10 minutes or until golden.
Garnish with thyme: Sprinkle with remaining thyme.
Stand 5 minutes then remove to serve. Use a tablespoon or butter knife to help scope them out. (Note 3)
To Serve: Dinner – serve as a side. Finger food – serve warm as is. Breakfast – serve with eggs and bacon.