Preheat the oven to 350 degrees F (175 degrees C). Grease a 9-inch round pie dish or cake pan.
Butter the bread on both sides and cut into triangles. Arrange a single layer of buttered bread in the bottom of the greased pan, slightly overlapping the triangles. Sprinkle with 1/2 of the sugar and all of the currants. Arrange the remaining bread on top, then sprinkle with remaining sugar.
Beat milk, eggs, and nutmeg together. Pour over the bread and press down firmly to compress the pudding and help the bread absorb the milk mixture.
Bake in the preheated oven until golden brown and set, about 30 minutes.