In a small bowl, stir together crumbs, cocoa and coffee. Add melted butter until well combined and wet. Press crumb mixture evenly into bottom and 2/3 the way up sides of a buttered 9-inch springform pan. Place pan on a cookie sheet and place in freezer.
In a large mixing bowl, combine cream cheese, sugar, and cornstarch. Using an electric mixer, beat until smooth but do not over beat. Add eggs and egg yolks one at a time, beating until incorporated after each. Stir in whipping cream. Stir in hot water and coffee. Add vanilla and melted chocolate. Pour mixture into crust. Bake at 350 F 15 minutes. Without opening oven door, reduce heat to 200 F, and bake 70 minutes or until center no longer looks wet and shiny. Remove cake from oven and run a thin knife blade around inside edge of pan. Turn oven off and put cake back in for another 60 minutes. Allow to cool at room temp and chill overnight.
Melt chocolate and shortening over low heat, stirring constantly. Stir in coffee until dissolved. Spread evenly over top of chilled cake.