Thinly slice the potatoes. You can do this with a mandolin if you wish, but a good sharp chef's knife and careful cutting will work just as well.
They should be tender enough to pierce with a knife, submerged in the cream but not falling apart.
Using a slotted spoon, transfer the potatoes, onions, and garlic to a bowl and allow them to cool slightly for easy handling.
Whisk cheddar cheese into the cream, warming on low heat if needed, to create a smooth sauce. Add dry mustard, cayenne, and season with salt & pepper to taste.
– Place on a baking sheet and cover loosely with aluminum foil. Bake for 35-40 minutes or until the potatoes are tender and the gratins are bubbling. Remove the aluminum foil 10 to 15 minutes before they're done so the cheese browns slightly.