Slice potatoes very thinly. Pre-heat oven to 190 C / 375 F / Gas Mark 5.
Grease dish well with half the butter.
Put cream, milk, thyme, crushed garlic and remaining butter in a small saucepan and simmer slowly.
Simmer for 20 minutes, remove from heat and let cool down slightly.
Strain sauce, and season with salt and pepper.
Lay potato slices in an overlapping pattern. Sprinkle some of the parmesan cheese between each layer. The top layer doesn't get any cheese.
Pour the cream sauce over the potatoes.
Cook for 50 minutes with a cover (aluminium foil or buttered parchement), then remove cover and leave on top shelf until golden brown.
Leave to cool for 10 minutes before serving.