In a large mixing bowl, combine the sugar and butter and mix until fluffy. Add the eggs, milk, vanilla and lemon extracts, and mix until smooth. In a separate bowl, sift together the flours, baking powder, and salt, and stir until mixed. Add the dry ingredients to the wet ingredients in batches, stirring well to combine.

Using a soup spoon, drop spoonfuls of the dough two inches apart on a baking sheet lined with parchment paper. Bake the cookies at 375 degrees until the edges begin to brown, about 20 to 30 minutes. Cool completely.

For the frosting: Place the powdered sugar in a large bowl. Gradually add enough of the boiling water to the sugar, stirring constantly, until the mixture is thick and spreadable.

Remove half of the frosting to the top half of a double boiler set over simmering water and add the chocolate. Warm the mixture, stirring, until the chocolate is melted and the frosting is smooth. Remove from the heat. With a brush or spatula, coat half of each cookie with chocolate frosting and the other half with white frosting.