For the meringues: Preheat the oven to 200 degrees F. Line a baking sheet with parchment paper and set aside. Add the egg whites to the bowl of a stand mixer fitted with the whisk attachment and beat the mixture on medium-high speed until the egg whites become frothy. Add the cream of tartar and continue to beat until the meringue make soft peaks 3 to 4 minutes. Add the sugar 1 tablespoon at a time, and continue to whip until the meringue until it makes stiff peaks, 5 to 6 minutes longer. Turn off the mixer, add the cocoa powder, and mix on medium speed until combined. Transfer the meringue to a piping bag (see Cook's Note below) and pipe long strips about the thickness of a pencil on the parchment paper-lined baking sheet. Place the meringue strips in the oven and bake until they are dry and crisp on the surface, about 2 hours. Remove the meringues from the oven and set aside to cool, then remove them from the parchment paper and slice them into 3/4-inch lengths.
For the dough: In a medium saucepan bring the buttermilk and vanilla powder to a boil over medium-high heat. Turn off the heat and let the mixture cool to lukewarm (the liquid should feel warm if you dip your finger in, but shouldn't be too hot to keep it in). Pour the cooled buttermilk mixture into the bowl of a stand mixer and stir in the yeast and sugar. Set aside until the yeast "blooms" at the surface of the milk and is bubbly and foamy, 5 to 10 minutes.
Add the flour, cinnamon and salt. Using the dough hook attachment, combine the mixture on low speed until there aren't many dry patches left. Add the eggs, one at a time, allowing the dough to come back together before adding the next egg, then slowly drizzle in the butter, mixing until completely incorporated. Increase the mixer speed to medium-low and mix until the dough is firm to the touch with a slight stickiness, about 5 to 7 minutes. Cover the bowl with plastic wrap and set aside in a warm, draft-free spot until it doubles in size, about 1 hour (when you press a thumb into the dough it shouldn't fill back in immediately but leave an impression).
Turn the dough out onto a lightly floured work surface. Dust the top of the dough with more flour, then roll the dough into a 1/2-inch thick sheet.
Fill a small bowl with flour and dust a parchment paper-lined rimmed baking sheet with flour and set aside. Dip a 3 1/2-inch doughnut cutter into the flour, then use it to stamp out a dough circle. Place the circle on the floured parchment-lined baking sheet. Repeat, stamping out as many circles as closely together as possible to yield about 24 circles (if reusing the scraps, gather them into a ball and let them rest in an oiled bowl for 1 hour before rolling the dough into a sheet and stamping out more doughnuts). Set the doughnuts aside in a warm, draft-free spot until they have nearly doubled, about 1 hour.
When the doughnuts are nearly ready, pour the oil into a large pot (or deep fryer) set over medium-high heat; the oil should fill the pot by about 3 inches--if it doesn't, add more. Heat the oil until it reads 375 degrees F on an instant-read thermometer. Add a few doughnuts to the hot oil, taking care not to overcrowd the pot (otherwise the doughnuts will stick together and not cook evenly). Cook until the doughnuts are golden, about 1 1/2 minutes, then use a slotted spoon to gently turn the doughnuts over. Fry on the other side until golden, about 1/2 minutes longer then transfer the doughnuts to a paper towel-lined baking sheet to cool. Repeat with the remaining dough circles, making sure the temperature of the oil comes back to 375 degrees F between batches.
For the glaze: Add the butter, milk and simple syrup to a medium saucepan set over medium heat, stirring occasionally. Once the butter is melted add the chocolate and vanilla and stir until smooth. Stir in the sifted confectioners' sugar until well combined, turn off the heat and set aside. (The glaze needs to be used warm, otherwise it will become too cool for glazing.) Dip the doughnuts in the chocolate icing, sprinkle with some chopped meringue and finish with chocolate shavings. Let the doughnuts set up for 5 minutes before serving.
If you don't have a piping bag, use a gallon-sized resealable plastic bag instead: simply fill the bag with meringue about 3/4 full, then snip off one corner of the bag to create a 1/2-inch opening.
A viewer or guest of the show, who may not be a professional cook, provided this recipe. It has not been tested for home use.