Preheat the oven to 350°F (175°C) and grease a 9x13-inch baking dish.
In a bowl, whisk together flour, baking soda, baking powder, and salt.
In another bowl, mix mashed bananas, sugar, melted butter, eggs, vanilla, and sour cream until smooth.
Add the dry ingredients to the wet mixture and stir until just combined.
In a separate bowl, combine brown sugar and cinnamon, then cut in the cold butter until crumbly.
Spread half of the batter into the baking dish, sprinkle half of the crumb mixture over it, then repeat with the remaining batter and crumbs.
Bake for 45-50 minutes, or until a toothpick inserted in the center comes out clean.
Cool slightly before slicing and serving.