In a small bowl, combine ginger and rum; set aside.
In a large heavy saucepan, combine the butter, cocoa and sugar. Cook and stir over medium-low heat until melted. Whisk a small amount of hot mixture into egg. Return all to the pan, whisking constantly. Cook and stir over medium-low heat until mixture reaches 160°.
Remove from the heat and stir in vanilla. Stir in the cracker crumbs, coconut, walnuts, cherries and ginger mixture. Press into a foil-lined 9-in. square baking pan.
For filling, in a large bowl, beat the butter, milk and pudding mix until blended. Gradually beat in confectioners' sugar until smooth; spread over crust. Freeze for 15 minutes or until set.
In a microwave, melt chocolate and butter; stir until smooth. Spread over top. Combine confectioners' sugar and milk; drizzle over top. Refrigerate for 1 hour or until set. Cut into bars. Yield: 3 dozen.