Cook the whole, unpeeled potatoes in boiling salted water for about 25 minutes or until tender. Drain.
When cool enough to handle but still warm, peel the potatoes and pass them through a mouli or ricer. It is important the potatoes are still warm at this stage.
Place the potato on a clean work surface, add the egg yolks and about ½ cup of plain flour. Fold the mixture together working towards the centre, gradually adding more flour if the mixture is too wet. Be careful not to add too much flour as the more flour added the firmer the gnocchi will be. Once the gnocchi mixture has come together rest for 5 minutes.
Cut the gnocchi mixture in quarters and on a lightly floured surface roll each piece into a sausage shape about 2cm/¾in in diameter, then cut into 3cm/1¼in pieces.
Place the gnocchi on a wooden board or floured tray. At this stage the gnocchi can be covered with a damp tea towel and left for 1-2 hours.
For the tomato sauce, heat the extra virgin olive oil in a frying pan, add the garlic and sea salt to taste and cook over a low heat for 2-3 minutes until pale golden.
Add the tomatoes and cook gently for 4-5 minutes. Add the basil and stir well.
Meanwhile, cook the gnocchi in gently boiling salted water for 2-3 minutes or until they float.
Drain the gnocchi and place in pasta bowls, spoon the sauce over and scatter with freshly grated parmesan.