Mix egg, milk and water. Slowly add the flour until the dough is rather firm. Let rest for 15 minutes, then knead for 2 minutes and let rest for another 10 minutes.
Tear off a small piece of the dough and shape it into a snake. Cut off small pieces with the knife and roll out about 1/2 cm thick with the rolling pin. Place small portions of mashed potatoes on top, shape into vareniki and cook in boiling salted water.