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Heat oven to 180C/160C fan/gas 6. Sprinkle the cut side of the remaining half of garlic with salt and use it to rub the inside of a large rectangular gratin dish. Lightly butter the dish. Melt the remaining butter in a saucepan.
Thinly slice the potatoes using a mandoline and stack them in piles. Tightly pack the stacks widthways in the dish, standing on their side, using only as many as will snugly fill the dish. Strain the warm cream over the potatoes, pressing down on the herbs as you do so. Bake for 1 hr or until the potatoes are cooked through and crisp on the top, brushing with the melted butter halfway through. Leave to cool for about 10 mins, then serve scooped straight from the dish.