Combine the flour, baking powder, salt, pepper, and nutmeg in a large mixing bowl. Make a well in the center and add the eggs and milk. Combine thoroughly, but do not overmix. Turn the dough onto a plate, cover loosely with plastic wrap and set aside for 30 minutes.
While the dough rests, bring a large pot of salted water to a rapid boil.
Start dropping teaspoon-sized portions of dough into the boiling water. You don't want to overcrowd the pot, so plan to work with no more than 1/4 of the dough at a time.
As the dumplings float to the surface, remove them from the pot with a slotted spoon and set aside.
Once all of the dumplings are cooked, drain the water from the pan and melt the butter over medium heat. Add the dumplings and toss in the melted butter to until they're heated through and nicely coated. Add a little extra seasoning if desired and serve immediately.