In a large bowl, stir the flour, eggs, milk and salt until smooth (dough will be sticky). In a large saucepan, bring water to a boil. Pour dough into a conlander or spaetzle maker coated with nonstick cooking spray, place over boiling water.
With a wooden spoon, press dough until small pieces drop into boiling water. Cook for 2 minutes or until dumplings are tender and float. Remove with a slotted spoon; toss with butter.