In a medium bowl, whisk the eggs, milk, mustard and a generous pinch each of salt and pepper. Whisk in the flour; the batter will be stiff. Refrigerate for at least 10 minutes or for up to 4 hours.
Set a colander with large holes (at least 1/4 inch) over a large pot of boiling salted water. Add the spaetzle batter and scrape it back and forth with a rubber spatula, pressing it through the holes into the boiling water. Stir the spaetzle once or twice to separate them and simmer until firm, 2 to 3 minutes. Drain in a clean colander.
In a large nonstick skillet, melt the butter. Add the spaetzle and cook over moderately high heat, tossing, until lightly golden, 5 minutes. Serve hot.
The spaetzle can be boiled 6 hours ahead. Sauté before serving.