Preheat oven to 375 degrees. Into a medium-size bowl, sift together flour, cocoa powder, baking soda, baking powder, and salt; set aside.
In the bowl of an electric mixer fitted with the paddle attachment, cream sugar and butter until light and fluffy, about 2 minutes. Add egg; beat to combine. With mixer on low speed, gradually add the flour mixture; continue beating until dough is well combined.
Using a 1 1/4-inch ice cream scoop, drop dough onto parchment-lined baking sheets about 2 inches apart. Dip bottom of a glass in sugar; press to flatten cookies to about 1/8 inch thick. (You may need to carefully remove dough from glass with a thin metal spatula.)
Transfer to oven, and bake until cookies are firm, about 10 to 12 minutes, rotating baking sheets halfway through. Transfer baking sheets to wire racks to cool completely.
Filling: In the bowl of an electric mixer fitted with the paddle attachment, cream butter and shortening until well combined. With mixer on low speed, gradually add the confectioners' sugar, and continue beating until light and fluffy, about 2 minutes. Add the vanilla, and beat to combine. Set aside at room temperature until ready to use.
Place cream filling in a pastry bag fitted with a coupler, and pipe about 1 tablespoon filling onto the flat side of half the cookies. Place remaining cookies on top, and gently press on each to squeeze filling to edges. Filled cookies can be stored in airtight containers at room temperature up to 2 days.