Combine the cookie crumbs, milk and 1/3 cup butter in a bowl and mix well. Press the cookie mixture over the bottom and up the sides of a 9-inch pie plate. Freeze until firm. Spread the vanilla ice cream in the frozen crust and freeze until firm. Spread the coffee ice cream over the vanilla ice cream layer and freeze until firm.

Combine the remaining ingredients in a double boiler and mix well. Cook over hot water until the mixture is thick, stirring constantly. Remove from heat to cool. Pour over the coffee ice cream layer and freeze until 10 minutes before serving.