Preheat Oven to 350 F (176 C) and line a 9 x 9 inch square baking pan with overhanging parchment paper.
In a medium bowl sift together both flour and cocoa powder. Add salt and stir gently with a hand whisk. Set aside.
Place chocolate chips in a large bowl, pour hot melted butter onto chocolate chips and let sit for a couple of minutes Then stir with a rubber spatula gently until chocolate and butter become smooth and silky.
Add sugars to the the melted chocolate mixture and stir with rubber spatula until mixed.
Next stir in vanilla and banana. Then add in each egg one at a time stirring and folding enough to incorporate.
Then add half of the flour mixture, folding in until there aren't any flour streaks. Add the banana rum cream and remaining flour. Fold until just mixed. Do not stir aggressively.
Scoop brownie batter into prepared pan. Evenly spread and level batter across the pan.
Place brownie pan on upper rack of oven and bake for 40 minutes. The brownies will be soft in the middle and firm as they cool. DO NOT over bake!
Place pan on cooling rack to cool for 20- 30 minutes before slicing. Or let completely cool and lift from tray by pulling up on side pieces of parchment paper.
Slice brownie into even thirds down both sides to make 9 large brownies.
Store cooled brownies in an air tight container at room temperature for 4 days.