Peel and wash the potatoes. Cook in salted water for about 20 minutes until soft. Chop tomatoes finely. Drain and steam the potatoes. Press potatoes still hot through a potato press. Stir in 1 egg, 3 egg yolks, tomatoes and butter.
Season with salt.
Preheat the oven (electric cooker: 200 °C/circulating air: 175 °C/gas: see manufacturer). Pour the potato mixture into a piping bag without a spout and spray approx. 30 longish croquettes onto a baking tray lined with baking paper.
Alternatively, form about 30 cams with two spoons. Whisk 1 egg yolk. Carefully brush the croquettes with it and bake in a hot oven for about 20 minutes.
Slice the cheese with the peeler. Remove potatoes from the oven and sprinkle with cheese shavings.