Soak the porcini in the boiling water for about 20–30 minutes.Preheat the oven to 220°C/200°C Fan/gas mark 7/450ºF. Heat the butter and garlic oil in a large pan.
Drain the porcini, reserving the liquid, then finely chop the mushrooms and add them to the pan to cook for a couple of minutes. Add the mushroom-liquid, milk, cream, star anise and salt and pepper.
Without peeling the potatoes or parsnips, slice them into 1cm round slices and add to the pan.
Bring the pan to a bubbling simmer and then gently cook, partially covered, for 20 minutes, or until the potato and parsnip are tender but not mushy.
Decant into a gratin-type, ovenproof dish (mine is a round shallow casserole, about 30cm x 7cm deep / about 5-quart capacity).
Cook in the oven for about 40 minutes (it will need longer if you have cooked it ahead and left it to cool before putting in the oven) or until the top is coloured in places and the gratin looks bubbly underneath.