In a medium bowl, whisk to combine the egg, salt, milk, and sugar.
Add the flour a spoonful at a time, stirring to combine with a wooden spoon or by hand until the dough begins to form. The mix by hand and start kneading the dough. If the dough is stiff before all of the flour is added, don't add any more flour.
Knead the dough on a floured surface until it is cohesive, about 5 minutes. This may take some elbow grease!
Turn the bowl used to mix the ingredients over the dough and allow it to rest for at least 30 minutes and up to 2 hours.
Use a floured rolling pin to roll the dough on a floured surface to a 10-inch circle (about 1/8-inch thickness). Lift and turn the dough as you roll.
Use a pizza wheel to cut into noodles. For soup, cut them about 1 to 1 1/2-inches long by 1/4-inch wide. Add them to boiling soup broth, a handful at a time, and cook about 10 to 15 minutes, until tender. Add more liquid (water or broth) to the soup if more liquid is needed after cooking the noodles.