Preheat oven to 350 degrees F. Line a 9 inch square metal pan with nonstick foil.
Melt butter in a saucepan over medium heat, then reduce heat to low and add the chocolate. Cook and stir over low until smooth. Remove from heat and stir in cocoa powder. Set aside and let cool slightly.
In a large mixing bowl, mash the banana until smooth. Whisk in the brown sugar, eggs and vanilla.
Add melted chocolate mixture to banana mixture and stir until combined, then stir in the salt and the flour.
Check to make sure mixture is not too warm, then add the chocolate chips.
Pour batter in the pan and spread evenly
Mix together peanut butter and oil and drop spoonfuls of peanut butter over the batter. Drag a knife through to make a marble pattern.
Bake for 30 minutes or until brownies appear set. While brownies are hot, drop small spoonfuls of peanut butter over the peanut butter marbled areas so they'll appear smooth again.
Let cool to room temperature, then chill for about 2 hours. Lift from pan and cut into squares.