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.

Preheat oven to 350 degrees with rack in lower third. Place almonds in a food processor; process until as fine as possible, about 1 minute. Add confectioners’ sugar; process until combined, about 1 minute.

Pass almond mixture through a fine-mesh sieve. Transfer solids in sieve to food processor; grind and sift again, pressing down on clumps. Repeat until less than 2 tablespoons of solids remains in sieve.

Whisk egg whites and granulated sugar by hand to combine. Beat on medium speed (4 on a KitchenAid) 2 minutes. Increase speed to medium-high (6) and beat 2 minutes. Then beat on high (8) 2 minutes more.

Add dry ingredients all at once. Fold with a spatula from bottom of bowl upward, then press flat side of spatula firmly through middle of mixture. Repeat just until batter flows like lava, 35 to 40 complete strokes.

Rest a pastry bag fitted with a 3/8-inch round tip (Ateco #804) inside a glass. Transfer batter to bag; secure top. Dab some batter remaining in bowl onto corners of 2 heavy baking sheets; line with parchment.

With piping tip 1/2 inch above sheet, pipe batter into a 3/4-inch round, then swirl tip off to one side. Repeat, spacing rounds 1 inch apart. Tap sheets firmly against counter 2 or 3 times to release air bubbles.

Bake 1 sheet at a time, rotating halfway through, until risen and just set, 13 minutes. Let cool. Pipe or spread filling on flat sides of half of cookies; top with remaining half. Wrap in plastic and refrigerate.

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.