Cream butter with lemon peel and juice; add sugar gradually, beating until fluffy.
Add egg and beat thoroughly.
Sift flour, baking powder, and salt together; add in fourths to creamed mixture, mixing until blended after each addition.
Mix in currants.
Chill dough thoroughly.
Roll a third of dough at a time 1/4 inch thick on a floured surface.
Cut with 2 1/2-inch fluted cutter.
Brush cutouts with milk; sprinkle with sugar.
Transfer to ungreased cookie sheets.
Bake at 350Â°F 12 to 15 minutes.