To make the cake, preheat the oven to 350°F. Butter a 9 x 13 x 2-inch baking pan with 1 tablespoon of the butter and set aside.
Dissolve the coffee in the hot water and let cool. Sift together the flour, cornstarch, baking soda, and salt onto a large sheet of waxed paper.
Cream the remaining 8 tablespoons butter and the sugar in a medium bowl with an electric mixer on high speed until light and fluffy, scraping down the sides as needed, about 3 minutes. Add the sour cream and mix well. In three additions, add the flour mixture, alternating with the eggs, beating well after each addition and scraping down the sides of the bowl as needed. Beat in the melted chocolate, dissolved coffee, and vanilla. Spread the batter in the prepared pan.
Bake until a toothpick inserted in the center of the cake comes out clean, 40 to 45 minutes. Cool on a large wire rack for 10 minutes. Carefully run a knife around the edges of the cake, invert onto the rack, and cool completely.
To make the icing, beat the butter in a large bowl with an electric mixer on high speed until fluffy, about 2 minutes. On low speed, beat in the sugar, about 1/4 cup at a time, until smooth. Add the cooled chocolate and vanilla and mix well. If not using immediately, cover tightly with plastic wrap until ready to use.
Slice the cake in half horizontally. Transfer the bottom, cut side up, to a platter. Spread half of the icing over the cake with a metal icing spatula. Top with the top half of the cake, cut side down. Spread the remaining icing over the top and sides of the cake. Sift the 1/4 cup confectioners’ sugar through a fine wire sieve to garnish, if desired. Serve at room temperature.
Yield: 12 servings