1. Sift the flour onto a board and make a well in the center.
2. Add the egg, water, and salt. Mix until the dough forms a ball. It should be very stiff, but if it will not stick together, you may have to add an extra teaspoon of water.
3. Knead well until the dough is smooth and elastic, about 10 minutes. Shape into a ball, cover with plastic wrap, and refrigerate for 1 hour.
4. Roll out the dough on a floured board until paper thin, and leave it to dry for about 30 minutes.
5. To slice the dough, either use a pasta machine, or roll it up like a jelly roll, and slice it crosswise at 1/4 inch or 1/16 inch intervals, depending on whether you want wide or thin noodles.
6. Shake the noodles to separate them, and hang them over a rack (or horizontal broom handle supported by 2 chairs) to dry in a warm, dry place, up to 3 to 4 hours.
7. When noodles are completely dry, store in a jar with a tight-fitting lid; they will keep as long as packaged noodles.
8. To cook, place noodles in rapidly boiling salted water: 5 minutes for thick, 2 minutes for thin.
9. Add noodles to boiling soup or use in noodle dishes.