1. Line a 9- x 5-inch loaf pan with two sheets of plastic wrap, leaving some wrap over-hanging the long sides. Sift the icing sugar and cocoa powder together into a bowl.
2. Whip the cream using an electric mixer on high speed until it holds soft peaks. Add the icing sugar-cocoa mixture and whip to combine.
3. Place enough graham crackers to cover the entire bottom of the prepared pan (break the crackers to fit.) Brush with some of the cooled coffee. Top with about ¾ cup of the chocolate whipped cream and spread into an even layer. Top with another layer of graham crackers and brush with more coffee. Spread with another ¾ cup of the chocolate whipped cream. Repeat, ending with a layer of graham crackers, until there are 5 layers of graham crackers in the cake in total. Brush the top with coffee and wrap with plastic wrap.
4. Refrigerate for at least 4 hours or up to 24 hours.
5. To make the glaze, sift the icing sugar and cocoa powder together into a medium bowl. Slowly stir in the coffee and vanilla, a little at a time, adding just enough to make a smooth, pourable glaze.
6. Unfold the plastic wrap on the cake, then place a serving platter over the loaf pan. Flip the pan and platter upside down, remove the pan and gently lift off the plastic wrap. Spoon glaze evenly over the top, letting a little bit drip down the sides. Chill until ready to serve. Slice thickly to serve.