Dice the potatoes, cook (uncovered) in salted water for approx. 20 mins. until soft. Drain the water. Push the potatoes through a sieve or mash them with a potato masher. Add the flour, butter and egg yolks. On a lightly floured surface, shape the dough into rolls the width of your finger, cut into approx. 2 cm long pieces. Boil the gnocchi in batches in salted water until they float to the surface. Remove, drain and keep warm.
Cut a cross into the tomatoes, pour over boiling water, peel and cut into pieces.
Press the garlic and sauté in the olive oil. Add the tomatoes, simmer for approx. 10 mins., season the sauce. Tear the basil and add it to the sauce at the end.
Spread the parmesan on a baking tray lined with baking paper. Preheat the oven to 200 °C (top heat only). Place the tray in the upper third of the oven and bake the cheese until it melts. Remove the tray from the oven, allow the cheese to cool a little, break into pieces.