Photo: Georgia Glynn Smith
Preheat the oven to 200°C/fan 180°C/gas mark 6. Place a buttered heavy-based ovenproof frying pan about 16cm diameter x 5cm deep over a low heat and carefully arrange a neat layer of overlapping potato slices on the bottom. Brush with some of the melted butter and season with salt and pepper. Continue to layer the potatoes, melted butter and seasoning until all the potatoes have been used.
Brush the potatoes with the remaining butter and season. Turn up the heat to medium and cook for a further 5 minutes or until you can see the sides beginning to crisp up. Remove from the heat and cover carefully with kitchen foil. Bake in the preheated oven for 40-45 minutes, or until the potatoes are tender, then remove from the oven and put a similar-sized plate on top of the pan. Weigh it down with two cans of beans, or similar, and leave to stand for 30 minutes to firm up.
Put the tomatoes on the baking tray, drizzle with the olive oil and season with salt. Roast in the oven for 15 minutes.
Meanwhile, heat a heavy-based griddle pan until very hot. Season and lightly brush each steak with oil. Griddle for 1 minute, then turn around to create a criss-cross marking and cook for another minute. Repeat on the other side. Leave the steaks to rest on a board or plate for at least 5 minutes before serving.
Put the vinegar and egg yolks in a small bowl over a small pan of gently simmering water. Whisk continuously until the mixture just thickens, then remove from the heat and whisk in the hot melted butter, a little at a time, until the butter is all incorporated – the sauce should be the consistency of loose mayonnaise. Add the tarragon, a squeeze of lemon juice and salt to taste.
Turn the potato cake on to a board. Arrange the garlic and parsley in the middle and cut into wedges. To serve, transfer the steaks to a warm plate and add a couple of potato cake wedges and some tomatoes. Eat with the béarnaise sauce on the side.