Cube the cold butter into small pieces. Add to a medium size mixing bowl.
Add the flour, brown sugar, and granulated sugar, and using your hands create small clumps then put them into the freezer until the cookies are done baking
In the bowl of a stand of a mixer with the paddle attachment, cream together the softened unsalted butter, brown sugar, and white sugar until light and fluffy.
Add the mashed banana, egg, and vanilla extract to the creamed mixture. Mix until well combined.
In a large mixing bowl, whisk together the all-purpose flour, cornstarch, salt, and baking powder.
Gradually add the dry ingredients to the wet ingredients, mixing until a dough forms.
Refrigerate the dough for 1-2 hours (the longer the better)
Preheat your oven to 375°F. Line a baking sheet with parchment paper or a silicone mat.
Using a large cookie scoop, drop the cookie dough onto the baking sheet
Bake the cookies in the preheated oven for 10-12 minutes. You'll want to take them out when they still look a little doughy in the middle. They will continue cooking on the baking sheet, and you want them soft in the middle.
Allow the cookies to cool on the baking sheet for 5 minutes, then take 1 tbsp of crumble topping and gently press into the top of each cookie. Make sure you don't do this as soon as they come out of the oven or the topping will melt into the cookie.
GLAZE
In a medium bowl, add the powdered sugar and milk and whisk until it forms a glaze.
Allow the cookies to completely cool and then drizzle the powdered sugar glaze over the top. Make sure they are fully cooled or the glaze will melt.