Preheat the oven to 350°F / 175°C. Butter a 7" springform pan and line the bottom with parchment paper.
In a small saucepan set over medium heat, brown the butter. Stir the butter occasionally until it turns amber in color and develops little brown specks.
Transfer the butter to a small bowl and set it in the freezer for 5 minutes to chill.
In the meantime, make the streusel.
Melt the butter in a small microwave safe mixing bowl. Add in the sugar, flour, and cinnamon and mix until well combined. Set the mixture in the fridge while you finish making the cake batter.
Add the banana to a medium sized mixing bowl and mash it until no large clumps of banana remain.
Add in the cooled brown butter, brown sugar, egg, vanilla, and greek yogurt. Whisk vigorously until the mixture is well combined.
Add in the flour, baking powder, and salt. Mix together until only a few flour streaks remain. Add in the mini chocolate chips, then mix just until no flour streaks remain.
Pour the cake batter into the prepared cake pan. Remove the streusel from the fridge and use your fingers to crumble it over the cake. Bake for 45-55 minutes, or until a toothpick inserted in the center of the cake comes out clean.