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Peel, trim and slice the potatoes a few hours ahead, and leave in cold water to stop them discolouring.
Preheat the oven to 200°C, fan 180°C, gas 6. Peel the potatoes and trim them into rectangular evenly-sized blocks. (Use the offcuts for mash or soup, just keep them in water until you need them). Using a mandoline, carefully slice the potatoes into 2mm-thick pieces. You can do this by hand with a sharp knife, but it may take a while. Keep the sliced potatoes stacked in order for a neater finished look.
Butter a nonstick baking tray with some of the butter and fan out the potatoes in lines, like fallen dominoes. They should mostly overlap, with just 2-3mm of each potato showing. Brush with most of the remaining butter, tuck in the bay leaves here and there, and scatter over the thyme leaves. Season generously and bake for 30 minutes.
Brush with the remaining butter, scatter over the cheese and bake for another 15-20 minutes until the edges are golden and crispy, and the cheese has melted. Scatter with more thyme, if you like.