Whisk together the flour, nutmeg, 1/2 teaspoon salt and a few turns of black pepper in a medium bowl. Whisk together the milk and eggs in a separate bowl. Whisk the egg mixture into the dry ingredients and stir to combine. Cover and refrigerate for 30 minutes.
Bring a large pot of salted water to a boil. Working in batches, press the spatzle dough through a greased spatzle maker or slotted spoon (the slots should be on the larger side, about 1/4- to 1/2-inch), using a rubber spatula, into the boiling water. Cook for 2 to 3 minutes. When the spatzle float to the top, remove with a slotted spoon and transfer to a medium oiled bowl.
Heat a large skillet over medium heat and add the butter. Heat until the butter melts and begins to brown. Add the spatzle and saute until they begin to brown slightly. Season with salt. Transfer to a plate and serve!