In a large bowl, combine the flour, salt, pepper, and nutmeg. In another mixing bowl, whisk the eggs and milk together. Make a well in the center of the dry ingredients and pour in the egg-milk mixture. Gradually draw in the flour from the sides and combine well; the dough should be smooth and thick. Let the dough rest for 10 to 15 minutes.
Bring 3 quarts of salted water to a boil in a large pot, then reduce to a simmer. To form the spaetzle, hold a large holed colander or slotted spoon over the simmering water and push the dough through the holes with a spatula or spoon. Do this in batches so you don't overcrowd the pot. Cook for 3 to 4 minutes or until the spaetzle floats to the surface, stirring gently to prevent sticking. Dump the spaetzle into a colander and give it a quick rinse with cool water.
Melt the butter in a large skillet over medium heat and add the spaetzle; tossing to coat. Cook the spaetzle for 1 to 2 minutes to give the noodles some color, and then sprinkle with the chopped chives and season with salt and pepper before serving.