In a large bowl, stir the flour, eggs, milk and salt until smooth (dough will be sticky). In a large saucepan over high heat, bring water to a boil. Pour dough into a colander or spaetzle maker coated with 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. If desired, sprinkle with parsley.