How to Make It
Preheat the oven to 325°. Butter a 10-by-15-inch rimmed baking sheet and line with parchment paper. Butter the paper and refrigerate until the butter is firm, about 15 minutes.
In a small saucepan, melt the butter and chocolate over low heat, stirring occasionally. Let cool.
In a medium bowl, beat the sugar and egg until blended. Beat in the coffee, vanilla and melted chocolate. Sift together the flour, cocoa, baking powder, cinnamon and salt. Stir the dry ingredients into the chocolate mixture until combined. Spraed the batter out to the edges of the baking sheet in an even layer; smooth the top. Bake for about 15 minutes, or until the center is just set but not dry. Let the chocolate wafer cool in the pan for 15 minutes.
Run a knife around the edge of the wafer. Cover the pan with a cutting board and invert; peel off the paper. Let the wafer cool completely.
Cut the chocolate wafer in half to form two 7 1/2-by-10-inch rectangles. Spread the ice cream evenly on one of the rectangles and cover with the other. Poke a few holes in the top with a fork or a toothpick for decoration. Wrap the ice cream sandwich in plastic wrap and freeze until firm, at least 2 hours.
In a small saucepan, melt the butter in the cream and milk over moderate heat. Stir in the sugar and boil, stirring occasionally, until slightly thickened, about 3 minutes. Remove from the heat and whisk in the cocoa until smooth.
In a small saucepan, combine the coffee and sugar and bring to a boil. Cook over moderately low heat until the syrup is slightly thickened and coats the back of a spoon, about 18 minutes. Remove from the heat; the sauce will continue to thicken as it cools.
To serve, cut the ice cream sandwich into 8 triangles. Drizzle the coffee sauce in a spiral on 8 dessert plates. Set an ice cream sandwich in the center of each and spoon the warm chocolate sauce on top.