Preheat the oven to 325°F and grease and line an 8×8 baking pan with parchment, leaving an overhang on the sides.
In a bowl, combine flour, cinnamon, and both sugars to make the crumble, then stir in the melted butter until it resembles wet sand.
Place this bowl in the refrigerator to chill.
In another bowl, whisk together the flour, baking soda, and salt.
In a large bowl, whisk together the sugars and softened butter until fully combined, then add the sour cream, egg, vanilla extract, and mashed banana.
Mix until smooth.
Gently fold the dry ingredients into the wet using a rubber spatula.
Spread half of the batter into the prepared pan.
Mix the cinnamon and sugar and sprinkle an even layer over the batter.
Top with the remaining batter and spread evenly.
Take the chilled crumble from the fridge and crumble it evenly over the top of the cake.
Bake for 40 to 45 minutes, or until a toothpick inserted in the center comes out with a few moist crumbs.
Let the cake cool for 30 to 40 minutes.
While it cools, whisk together the powdered sugar and milk until it reaches a glue-like consistency, adjusting with extra milk if needed.
Drizzle the icing over the slightly warm cake and serve.