To make the Chocolate Pudding: Combine 1 cup milk with 2 tablespoons sugar in a small saucepan and bring to just under a boil.
In a mixing bowl, combine remaining sugar with salt, cocoa, and cornstarch. Whisk in remaining 1/2 cup unheated milk. Gradually whisk in hot milk and place entire mixture back into the saucepan. Heat, over medium heat, stirring, until mixture thickens and just starts to bubble.
Whisk in egg and egg yolk and cook, stirring, for 30 seconds. Remove from the heat and whisk in chopped chocolate and butter. When both are melted, strain pudding through a fine-mesh strainer, and cool. Cover with plastic and reserve in refrigerator.
To make the Cake: Preheat oven to 350 degrees F. Lightly butter 2 (8-inch) cake pans and line with parchment. Butter the parchment and flour pans, shaking out the excess.
Sift together flour, cocoa, baking soda, baking powder, and salt. Reserve.
In a mixer with a whip attachment, beat eggs and sugar until thick and lemon-colored. Beat in vegetable oil. Alternately add dry ingredients with buttermilk, scraping the bowl once or twice. Add the coffee and vanilla to form a thin batter. Divide between prepared cake pans.
Bake until a toothpick inserted in the center of a cake comes out clean, about 40 to 45 minutes. Cool in pan for 15 minutes. Invert onto cooling racks, peel off paper and cool completely.
When cool, split each cake in half with a serrated slicing knife. Reserve 1 layer for another use. Spread bottom layer with half of the reserved Chocolate Pudding. Place second layer on top and spread with remaining pudding. Top with last cake layer.
To make the Icing: Over a double boiler, melt chocolate with butter. Remove from heat, whisk in brewed coffee, corn syrup, and vanilla. Place icing over an ice bath and chill, whisking often until the mixture is of soft but a spreadable consistency. Working quickly, ice the sides and top of cake.
In a food processor, pulse the cookies into crumbs. Press the crumbs onto sides and top of cake.
Serve cake at room temperature. If holding for more than 2 hours, store in refrigerator for up to 48 hours, but bring to room temperature before serving.
Serving Suggestion: Blackout cake is meant to be served simply, on its own. If you want to dress individual plates, perhaps add a drizzle of fudge sauce and a sprinkle of cocoa powder.
Recipe courtesy of Karen Barker, Sweet Stuff: Karen Barker's American Desserts, University of North Carolina Press, 2004