Make the macaron shells: sift together the almond flour, powdered sugar, and cocoa powder. Repeat a second time. Discard any large chunks of almond flour left in the sifter.
In the bowl of a KitchenAid mixer fitted with a whisk attachment, beat the egg whites on medium speed until frothy, about 1 minute. Add the cream of tartar. Slowly add the granulated sugar and increase speed to the highest level until the egg whites form firm peaks but are not dry, about 5 to 7 minutes.
Sift the almond flour mixture into the whipped egg whites. Fold the ingredients together until the mixture becomes shiny and somewhat loose. It will ooze slightly in the bowl and should have the consistency of melting ice cream. Spoon the mixture into a pastry bag fitted with a small round tip.
Pipe out 1-inch rounds about an inch apart on an ungreased baking sheet lined with parchment paper. Let rest for 30 minutes until a skin forms on the outside of the shell and the surface looks dry.
Preheat the oven to 300°F. Bake the macarons for 10 to 12 minutes. When the bottoms do not stick to the parchment paper, they are done.
Make the marshmallow filling: in the bowl of a KitchenAid mixer fitted with a paddle attachment, cream the butter and shortening together. Slowly add the powdered sugar and whip until light and fluffy, about 5 minutes.
To assemble: spoon the marshmallow filling into a pastry bag fitted with a small round tip and pipe a small amount of filling onto the bottom of a macaron shell. Top with another macaron to make a sandwich. Repeat with the remaining macarons and filling.