In a small mixing bowl, combine flour and 1 teaspoon salt. Create a well in center of flour mixture. In a separate bowl, whisk together eggs and milk. Pour into flour well and mix slowly until a smooth batter comes together.
Bring a large pot of salted water to boil. Using a rubber spatula, push batter through a large-holed colander (or a spaetzle maker) into boiling water. Cook until spaetzle float to the surface; then use a slotted spoon to transfer to a bowl. Season with salt and pepper; toss with melted butter and parsley. Spoon a generous portion of spaetzle onto warmed serving plates.
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