Preheat your oven to 350 degrees. Generously grease an 8-inch round or square cake pan, and line it with parchment paper that has overhangs for easy removal. Set aside.
In a large bowl, beat together the butter and sugar until fluffy and well-combined. Beat in the eggs and vanilla extract, and then add in the mashed bananas until just combined. Finally, add in the flour, baking soda, and salt, and beat until there are no dry pockets of flour, and you have a thick batter. It will have a few small lumps in it depending on how over-ripe your bananas are- that's ok!
Spread about half of the batter evenly into your prepared pan, and then make the cinnamon/sugar filling.
In a small bowl, stir together the brown sugar and cinnamon until well combined. Sprinkle the entire mixture evenly over the half of the batter in your prepared pan already. You want the mixture to be pretty even, and to cover the entire layer of batter.
Dollop the remaining cake batter on top of the cinnamon sugar mixture to make it easier to spread, and then use the back of a spoon or a small offset spatula to spread the batter all the way to the edges, covering the cinnamon mixture completely.
In a medium bowl, using a fork, stir together the butter, flour, brown sugar, cinnamon, baking powder, and salt until a crumb starts to form. This may take a few minutes and a little working with the fork. You want the mixture to form large crumbs when pressed together.
Sprinkle the crumb mixture evenly all over the top of the cake batter. Bake the cake in your preheated oven for 55-65 minutes, or until a toothpick inserted in the center of the cake comes out clean. Cool in the pan for 30 minutes, and then remove by pulling it out with your parchment paper over-hangs. Slice and enjoy!