In a wide, shallow bowl (or directly on a floured kitchen counter), peel and grate the potatoes, making sure you mash any larger bits that couldn't be grated. Add the flour, salt and paneer. Give the mixture a very quick stir. Make a well in the center and pour the egg in it. Use a fork and whisk the egg into the rest of the ingredients, starting from the center, going outwards. The dough will be crumbly, but soft.
Use a silicone spatula or your hands to bring the dough together, then drop it on a floured surface (or a silicone mat, which I find easier) and lightly knead it to make a soft dough. Do not over-knead, stick to about 30 seconds.
Pat the dough down into a loaf shape, roughly 9x4. Slice it vertically into long pieces. Roll each piece into a long 'rope' using lightly floured fingertips, then cut it into pieces, about 1 inch long. These measurements don't have to be perfect, just make sure you don't cut pieces that are too thick or too long, otherwise they get difficult to eat. Bite-sized is best. Keep the pieces on a lightly floured surface (or another silicone mat), making sure they don't touch. For a little added fun and to help the sauce stick better to the gnocchi, press a fork down lightly into each one to make an indentation.
Bring a pot of salted water to boil. Drop in a few pieces at a time, making sure the water is simmering continuously. In a minute or two, the gnocchi will rise to the surface and have slightly ragged edges. Take them out with a slotted spoon and set aside. Repeat with the rest of the dough.
Reserve 1 cup of the gnocchi water for the sauce.
Now drizzle a couple of spoonfuls of olive oil onto a hot frying pan, preferably non-stick. Pat the gnocchi dry to absorb any remaining water, then place in the pan and cook till golden-brown on both sides. Set aside while you make the sauce.
In a pan, heat the olive oil, then add the garlic and fry till browned. Add the tomatoes and cook till they start to darken and caramelise. Press down on them to release juices and create a saucy base.
Add the basil, stir, then add the wine. Increase the heat to high and boil till the liquid has reduced to about a third.
Finally, add the pasta water and simmer till it thickens a bit. although overall, the sauce is runny. Add salt and pepper and stir well.
Pour into bowls and add the gnocchi on top. Stir and enjoy!