Fill a large pot halfway full with water and bring to a boil. Adjust heat so water just simmers.
Meanwhile, mix together flour, nutmeg, salt, and white pepper in a medium bowl.
Whisk eggs together in a small bowl. Add eggs alternately with milk to dry ingredients. Stir until smooth.
Working in batches, press dough through a spaetzle maker, or through a large-holed colander or metal grater, into simmering water. Cook 5 to 8 minutes. Remove with a slotted spoon or spider and drain well.
Melt butter in a large skillet. Add spaetzle and cook, stirring gently, until heated through. Serve sprinkled with parsley.