Combine eggs and milk in a large mixing bowl. Add salt and nutmeg. Using a wooden spoon, slowly combine the flour with the liquid. Mix until well combined.
Heat a large quantity of salted water to a full boil. Using a spätzle strainer, press the batter through the strainer with a rubber spatula into the water. When the cooked dough rises to the surface, remove with a slotted spoon and drain. Work in small batches.
When all of the dough is over, return all of the dough back to the boiling water and cook for 2 minutes. Drain well and mix with oil to keep the individual pieces separate.
Melt butter in a large sauté pan over high heat and sauté cooked dough until warm and a few pieces start to brown.