Heat the oven to 190°C fan, or 210°C conventional. Grease your baking dish generously with butter. Rub the inside with the cut sides of the garlic cloves, then discard them or save them for another use.
Soften the Leeks
Place the butter and olive oil in a saucepan over medium-low heat. Add the sliced leeks with a small pinch of salt and cook gently for 8 to 10 minutes, stirring now and then, until soft and sweet without colouring.
Warm the Cream Mixture
Pour the milk and double cream into the pan with the leeks. Add the thyme, nutmeg, fine sea salt and black pepper. Warm for 2 to 3 minutes until steaming but not boiling. Stir in half the gruyere.
Slice the Potatoes
Peel the potatoes and slice them into rounds about 3 mm thick. Try to keep them even so the gratin cooks uniformly.
Build the Layers
Arrange a layer of potatoes in the base of the dish, slightly overlapping. Spoon over a little of the leek cream mixture. Repeat until everything is used, finishing with a little liquid over the top. Press the layers down gently with the back of a spoon.
Add the Cheese Topping
Scatter over the remaining gruyere and the parmesan. Cover loosely with foil and bake for 40 minutes.
Finish Until Golden
Remove the foil and bake for another 25 to 30 minutes, until the top is deeply golden and the potatoes are completely tender when pierced with a knife. Leave it to rest for 10 to 15 minutes before serving. Finish with chopped chives if you like.
Notes
Floury potatoes work well here because they soften into the cream and help the layers settle into each other. You still get shape, but the texture becomes silky around the edges rather than waxy and separate. I slice them fairly thin, though not paper thin. Too thin and the layers collapse into mush. Too thick and the centre takes too long to tenderise.Gruyere is the main cheese because it melts beautifully and has a nutty, savoury flavour that stands up to the dairy. Parmesan is there in a supporting role, mostly for extra savoury depth and a better top crust. The leeks need washing carefully because they love trapping grit between their layers, which is one surprise nobody needs at dinner.