Preheat the oven to 180°C.
Place all the cheeses into the Thermomix bowl and mill 10 sec/speed 9 Remove from bowl and set aside.
Dollop some butter in a baking dish. Slice the leek and potatoes quite thinly and layer them into the dish with some grated cheese in between layers. Season as you go. Reserve a little cheese for the top.
Pour the cream around the edges of the vegetables so as not to disturb the layers. Let it sink through the layers. Repeat with the milk until you are confident all of the potatoes are covered with milk, other than the very top layer.
Finish off with the cheese and cover loosely with baking foil. Bake for 45 minutes until potatoes are well softened and the dish is fragrant. Remove the foil and finish cooking until golden and crispy on top, about 15-20 minutes more.
Serve before cold, but not too piping hot either. Potatoes stay very hot for quite a while.