Preheat the oven to 200C/190C fan/Gas 6 and put a metal baking sheet in it. Cut the fish into slices about 4cm thick.
Slice the tomatoes finely. You don’t need to save the juice – leave whatever runs out on to the cutting board as you don’t want the slices to be too wet.
Slice the potatoes finely too – you don’t need to peel them – using a mandolin if you have one. It’s important that the slices are really wafer-thin otherwise the potatoes won’t cook in the time given, which means your fish will be overcooked.
Layer up half the potatoes and half the tomatoes in a gratin dish, seasoning and sprinkling on the thyme as you do so.
Heat the cream and the garlic to boiling, strain the cream and pour half of this over the vegetables. Lay the fish on top, then add the rest of the vegetables and pour over the remaining hot cream. Sprinkle the cheese on top.
Bake in the oven – slide the gratin on to the hot baking sheet – for 40-45 minutes, or until the potatoes are tender.