Preheat your oven to 180°C (355°F).
Stick the muffin tin in the oven to warm up.
Wash and peel the potatoes.
Slice the potatoes finely on a mandolin. You want to be able to bend the thin slices without them breaking.
Remove the muffin tin from the oven.
Divide the butter into ten equal cubes and place one in each void.
When the butter is melted, brush it around the inside of the muffin tin cavities.
Then, layer the potato slices almost to the top of the pan. Spread them out as much as possible.
Season with sea salt and pepper every five slices or so.
Then, layer the smaller slices and arrange them so they overlap.
Push the slices down along the edges to get that closed rose shape.
Finish with 5-6 overlapping pieces, leaving a small gap in the center.
Mix the cream, minced garlic, mustard, sea salt, pepper, and thyme.
Pour spoonfuls of the cream mixture onto each potato stack until the cream reaches the top of the sides.
Bake the stacks for around 35 minutes until golden and tender.
Allow to set in the hot tin for 10-15 minutes (this helps them hold their shape).
To remove the potatoes from the pan, use a knife to loosen them from the edge, and then lift them carefully with a spoon.
Sprinkle with fresh chopped green onions or thyme.