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Put the milk, cream, garlic, a sprig of thyme, the nutmeg and horseradish into a pan and bring to a simmer. Remove from the heat, then leave to infuse for at least 10 mins.
Peel the potatoes and cut into slices the thickness of a £1 coin. Peel the parsnips, cut into quarters lengthways and discard the cores, then slice thinly lengthways. Heat oven to 180C/160C fan/gas 4.
Use 1 tbsp butter to grease a large baking dish, then layer up the potatoes and parsnips, adding a few thyme leaves and some seasoning with each layer. Remove the thyme sprig and garlic from the cream, then pour it all over the dish. Scatter over more thyme leaves, the breadcrumbs and the rest of the butter in little knobs. Cover with foil and bake for 1 hr, then uncover and finish for 25-30 mins more until the potatoes are soft, and the top is golden and bubbling.
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