Mix flour, baking powder, and salt in a medium bowl. In a large bowl, mash bananas and blend in butter, then add sugar, eggs, and vanilla. Stir in flour mixture and milk.
Combine cold butter, light brown sugar, and flour in a separate bowl. Blend them using forks or a pastry blender until coarse crumbs form. Pour half of the cake batter into the greased pan and top with half of the crumb mixture.
Add the rest of the batter over the crumb topping, then finish with the remaining topping. Bake in the oven for 55 minutes until the center sets. Let it cool for about 10 minutes before serving.