Bring a large pot of salted water to a boil. In a medium bowl, beat the eggs with the milk, mustard, chives, salt and nutmeg. Add the flour and stir until a sticky batter forms.
Scrape one-third of the batter into a large colander with 1/4-inch holes. Working over the pot of boiling water, scrape the batter across the bottom of the colander with a rubber spatula to press it through the holes. Gently stir the simmering spaetzle, then press the remaining batter through in 2 batches. Stir gently and simmer the spaetzle until cooked through but slightly chewy, 1 to 2 minutes. Drain the spaetzle in a clean colander.
In a large skillet, melt the butter over moderately high heat. Add the spaetzle and cook, stirring frequently, until thoroughly coated. Transfer the spaetzle to a bowl and serve right away.
The spaetzle can be prepared through Step 2 several hours ahead and sautéed just before serving.