In a medium bowl, combine cookie crumbs and 1/4 cup melted butter. Press the mixture on the bottom and up the sides of a 9-inch pie plate. Place in freezer.
Peel and slice bananas into 1/4 inch slices. Heat 1/4 cup butter in a large, heavy skillet until melted. Turn off heat and add the dark brown sugar, the rum, and the cinnamon. Turn heat back on to medium, and whisk and cook until mixture begins to bubble. Let cook for 3 minutes whisking often. Turn off heat. Add bananas and toss gently to coat with sauce. Remove crust from freezer and, using a slotted spoon to drain off most of the sauce, carefully place the bananas in the bottom of the crust. Pour the remaining sauce in skillet into a small container or bowl to cool to room temperature. (I like to use a container with a spout on it for easy drizzling later.) Place pie in freezer while filling is being made.
Beat the cream cheese, melted white chocolate, and the powdered sugar on high speed with a whisk attachment until fluffy. Beat in the peanut butter. Fold in the whipped topping by hand. Spread mixture carefully over bananas in pie crust covering fully. Place in freezer for 45 minutes to one hour. Remove pie from freezer and garnish with white chocolate curls, if desired. Cut into 8 slices and drizzle each slice with the reserved rum sauce. (If sauce gets too thick, just place in the microwave for 10-15 seconds.)