Trim fennel tips and remove outer leaves if these are tough or discoloured. Reserve any feathery bits and chop - they can go into the gratin.

Quarter each head of fennel length ways and carefully remove the hard core from each segment. Using a mandolin if you have one (it's much easier than a knife), cut the fennel into wafer-thin slices. Cut potatoes into wafer-thin slices, then place in a saute pan with fennel, double cream, sour cream, milk, salt and pepper. Bring to the boil, then reduce heat to low and let potatoes and fennel cook gently for about four minutes.

Preheat oven to 180 degrees. Butter a gratin dish and rub with halved garlic clove. Mix mustard through potato mix, then spoon mixture into gratin dish, season well and sprinkle over the reserved fennel fronds. Bake for one hour 20 minutes. The vegetables should be tender, the milk absorbed and the top golden brown.

Sprinkle parsley over and serve.