Combine the flour, baking powder, salt, and black pepper in a bowl. Whisk in eggs and milk and beat to create a batter that is cohesive but is still loose enough to be pushed through a sieve to make dumplings with identifiable strands of batter. (Add additional flour if too loose or additional milk if too dry.)
Bring a pot of water to boiling and reduce it to a simmer. Drop tablespoons of the batter into a strainer held over the boiling water to make the spaetzle "dumplings." Remove them to a platter with a slotted wooden spoon as they rise to the surface.
Melt butter as needed over medium-low heat in a saute pan to briefly saute the spaetzle.
Transfer to a serving dish and sprinkle with parsley.