Preheat the oven to 350 degrees F. Combine the crumbs, ground coffee and butter together. Mix well and press into a 10-inch spring-form pan. In a large food processor, with the metal blade, process the cream cheese until smooth. Add 1 1/2 cups of the sugar and blend. Add the eggs one at a time to thoroughly incorporate into the cheese mixture. Add 2 shots of the espresso and 1/2 cup of the heavy cream. Add the flour, salt and vanilla and blend until smooth. Pour into the prepared pan. Bake for 1 hour and 15 minutes or until the cake is set.(If you inset a toothpick in the center of the cake, it will not come out clean. After the cake will continue to cook as it is cooling.) If the cake starts to get too dark on the top, place a sheet of aluminum foil over the top of the cake. Remove from the oven and with a knife loosen the sides from the pan. This will prevent the cake from splitting down the center. Completely cool the cake before cutting. In the bowl of an electric mixer, fitted with a whip attachment, combine the remaining 1/2 cup sugar, shot of espresso, 1 cup cream, and coffee liqueur. Whip the cream to medium peaks. Slice the cake into twelve slices. Spread the whipped cream evenly over the top of the cake. Garnish each slice with the espresso beans and fresh mint sprigs.