In the bowl of a stand mixer, cream together the butter and sugar until light and fluffy. Beat in the egg until well combined.
In a small bowl, combine the flour, cocoa powder, and salt. Stir to combine. Slowly add the dry ingredients to the wet and beat until just combined.
Refrigerate the dough for 20 minutes or until easy enough to handle. Roll the dough into 1 inch balls. Place on a parchment lined baking sheet and press your finger tip into the center of each ball to form an indention.
Bake in a preheated 350 degree oven for 10 minutes. Remove from oven and cool completely before filling.
To make the frosting, beat together all of the ingredients (aside from the salt) with a mixer until light and fluffy. Pipe the frosting in to the indention of each cookie. Sprinkle with Fleur de Sel.