Preheat oven to 350 degrees and grease a 13X9-inch baking dish.
In a medium pan, cook the mashed bananas, 3 tablespoons rum, 1/2 cup brown sugar, and 1/4 cup butter until butter is melted and mixture is bubbly. Remove from heat and stir in vanilla extract and 1/4 teaspoon cinnamon. Let cool.
Using an electric mixer, beat cream cheese and 1/2 cup softened butter until smooth and creamy.
Add 1 cup brown sugar and beat until fluffy.
Add eggs one at a time. Stop to scrape down sides of bowl to get everything mixed evenly.
In a medium bowl, combine flour, salt, baking powder, and baking soda. Add to cream cheese mixture and beat on low until combined.
Stir in banana mixture and pour batter into prepared pan.
In a bowl, mix together pecans, 1 teaspoon cinnamon,1/2 cup brown sugar, 1/4 cup flour, and melted butter. Sprinkle on top of batter.
Place in oven and bake for about 45 minutes, or until a toothpick inserted in middle comes out clean.
Meanwhile make rum sauce. In a small saucepan, bring heavy cream to a simmer. In a small bowl, whisk together rum and cornstarch. Add to heavy cream and whisk well. Continue to whisk and cook until thickened. Remove from heat and whisk in 1/2 cup granulated sugar.
To serve, cut coffee cake into squares and drizzle with rum sauce.