Place the pecans in the oven and toast them for about 8 minutes. Check frequently because they will burn easily; set aside. Leave oven on.
Melt 1 tablespoon of the butter in a nonstick skillet over medium heat. Stir in the brown sugar and cook, stirring frequently, until melted. Add the sliced bananas and continue cooking until the bananas are caramelized and soft enough to be mashed with the back of a spoon. Remove from heat and set aside. If using, stir in the rum.
Combine the fat-free cream cheese, light cream cheese and 3/4 cup of the sugar in a large bowl and mix until completely blended. Add the sour cream, egg and egg whites and mix well. Add the caramelized banana mixture and again mix well.
Put the remaining tablespoon of butter, remaining 1/4 cup sugar and toasted pecans in a food processor fitted with a metal blade.
Grind until the consistency of fine gravel and put the mixture in the bottom of an 8-inch springform pan. Pack it down firmly using the palm of your hand.
Pour the filling mixture over the crust.
Place the pan in a large pan and add water to a depth of 2 inches.
Bake in the preheated oven for about 1-1/2 hours, or until firm to the touch.