cupsifted confectioner's sugar, plus more for dusting
tablespoonsunsalted butter, at room temperature
teaspoonpure vanilla extract
Using an electric mixer, cream the sugar, butter and salt at high speed until well blended, about 3 minutes. Scrape down the bowl, add the egg and vanilla and beat for 1 minute.
Beat in the cocoa at medium speed until thoroughly blended. Add the flour and mix at low speed just until incorporated.
Divide the dough in half; shape into 2 disks. Wrap in wax paper; refrigerate for 20 minutes.
Preheat the oven to 350 degrees . Line 2 cookie sheets with parchment. 1 roll out 1 dough disk 1/8 inch thick between sheets of wax paper. Rub cocoa on a work surface. Remove 1 sheet of wax paper. Flip the dough onto the surface; peel off the other sheet of wax paper.
Using a 3 1/4-inch snowflake cookie cutter, cut out cookies. Using an offset spatula, transfer the cookies to the prepared pans, spacing evenly. Repeat with the remaining dough disk.
Bake 1 pan at a time (refrigerate the other pan) until the cookies are set at the edges, 10 minutes. Let the cookies cool on the pans for 1 minute; transfer to racks to cool completely.
In a bowl, mix the sugar, butter, vanilla and salt.
Spread 2 tsp. of the frosting on the flat side of half of the cookies; sandwich with the remaining cookies. Dust with more sugar.