Preheat the oven to 200°C/400°F/ gas 6. Fry the potatoes in a heavy pan with the fat of choice over a medium heat, tossing and shaking until they are just starting to brown. This takes about 20 minutes.
Brush a 23-cm / 9-inch pan with butter, then season the partially cooked potatoes with salt and pepper and transfer them to the pan, pressing down gently with a spatula. Brush the top with more melted butter and put to bake in the preheated oven for 20–30 minutes, until the surface is golden brown.
Mix the garlic and parsley. Unmould the cake by placing a plate upside down on top of the pan then inverting them together. Strew the garlic and parsley mixture over the top and serve piping hot.