3/4cupsifted confectioner's sugar, plus more for dusting
4 tablespoonsunsalted butter, at room temperature
1/2teaspoonpure 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.