Combine 1 cup flour, salt, the egg and stir to combine.
Add water, a little at a time, and continue to stir until the mixture is smooth and has a stretchy consistency. This should take about 4-5 minutes of steady beating. The dough should be thicker than pancake batter and should stretch when lifted with a spoon.
Run a cutting board under water to wet the surface, then spoon a large dollop of dough onto the board.
Cut a ribbon about an 1" thick from the dollop, and using a kitchen knife, cut and slide 1/4" pieces into the boiling water.
The dumplings will rise to the surface when they are cooked.