Preheat oven to 325 degrees. Place pecans on baking sheet; toast in oven about 8 minutes. Check frequently to avoid burning; set aside.  Leave oven on. Melt 1 tbl. of the butter in non-stick skillet over medium heat.  Stir in brown sugar; cook, stirring frequently, until melted, about 6 minutes. Add 2 sliced bananas; cook until bananas are caramelized and soft enough to mash with back of spoon. Remove from heat; set aside.  Stir in rum, if using combine cream cheese and 1c of sugar in large bowl of electric mixer.  Beat until completely blended.  Add sour cream, eggs, vanilla and heavy cream, add caramelized banana mixture; beat until incorporated. Put remaining tbl. of butter, remaining 1/2 c sugar and toasted pecans in food processor fitted with metal blade.  Process until finely ground; press on bottom of ungreased 8-inch springform pan.  Pack down firmly using palm of hand. Pour filling mixture over crust.  Place pan inside larger pan and put on oven rack.  Add water to depth of 2 inches. Bake until firm to touch, about 1-1/2 hours.Remove from oven; let sit on wire rack 1 hour.  Refrigerate, covered, at least 3 hours or overnight before serving.