Cream together sugar and shortening. Add egg and vanilla and mix until combined.
In a separate bowl, stir together flour, salt, and baking powder. Add to wet ingredients and alternate with milk a little at a time and mix until thoroughly combined. The mixture will resemble a thick cake batter.
Scoop and drop onto lined cookie sheet. Shake cookie sheet slightly to allow batter to settle.
Bake for 10 to 12 minutes and remove from oven. Allow cookies to sit on pan for a minute or two before removing and placing on a wire rack to cool.
Turn the cookie over and frost the back side of the cookie with vanilla frosting on one half and chocolate frosting on the other half. I usually put on a thin layer of frosting, a crumb layer, at first and let it firm up. Then I add a second layer. This keeps the crumbs from mixing into the top layer of frosting and makes the cookies prettier.
Combine all ingredients except the cocoa. Beat until smooth.
Divide mixture in half. Add melted chocolate to half of the frosting and stir well. Keep the frosting slightly warmer than room temperature for easier spreading.