Cook the potatoes in plenty of boiling salted water. Peel and while they are still hot crush them with the potato masher (Italian ones look like very large garlic crushers: do not use a food processor or it will liquify the potatoes!).
Add the flour and work it into the mixture, using a fork so as not to burn your fingers, then work in the egg. Form long thin rolls with the mixture by dividing it into several pieces, placing them on a work surface and rolling the palm of your hand backwards and forwards on them.
When they are the thickness of a finger, cut into 2 cm. (1/2 inch) knobs. To make them a pleasant shape you can either pass them gently over a cheese grater or over the tines of a fork, pressing gently with your thumb. This helps to curl them.
Bring water to the boil in a large saucepan and throw in the gnocchi.
They are ready when they float, after a minute or two. Do not leave them too long or they will fall apart. Remove them from the water with a skimmer and place them into the serving bowl.
If you do not cook them immediately you should place them in one layer on a plate and sprinkle them with flour so that they do not stick to each other. Refrigerate.
They can also be deep frozen (de-freeze before cooking).