Preheat and Prep: Preheat your oven to 350°F (175°C). Grease and flour a 9-inch round cake pan and set it aside.
Brown the Butter: In a medium saucepan over medium-low heat, melt 1/2 cup (115g) of unsalted butter. Continue cooking, stirring frequently, until the butter turns golden brown and develops a nutty aroma. This should take about 5-7 minutes. Be careful not to burn the butter. Remove from heat and let it cool for 5-10 minutes.
Mix Wet Ingredients: In a large mixing bowl, combine the browned butter with 1 cup (200g) of brown sugar. Beat until well combined. Add in 1 large egg and 1 tablespoon (15ml) of vanilla extract, mixing until smooth. Stir in the mashed bananas until fully incorporated. Then, add 1/4 cup (60ml) of milk and 1/4 cup (60g) of sour cream or Greek yogurt, mixing until the batter is smooth.
Prepare Dry Ingredients: In a separate bowl, whisk together 2 cups (240g) of all-purpose flour, 1 teaspoon (4g) of baking powder, and 1/4 teaspoon (1g) of salt.
Combine Wet and Dry Ingredients: Gradually fold the dry ingredients into the wet ingredients, mixing until just combined. Be careful not to overmix, as this can result in a dense cake.
Layer the Cake: Pour half of the cake batter into the prepared 9-inch round cake pan, spreading it evenly.
Make the Crumble: In a medium bowl, combine 6 tablespoons (85g) of melted butter, 2/3 cup (133g) of brown sugar, 3/4 cup (95g) of flour, and 2 teaspoons (4g) of ground cinnamon. Mix until the ingredients are well combined and form a crumbly texture.
Assemble the Cake: Sprinkle half of the crumble mixture evenly over the batter in the cake pan. Then, pour the remaining cake batter over the crumble layer, spreading it gently. Top with the remaining crumble mixture.
Bake: Bake in the preheated oven for 45 to 55 minutes, or until a toothpick inserted into the center of the cake comes out clean.
Cool and Slice: Allow the cake to cool in the pan on a wire rack for about 15 minutes. Then, remove the cake from the pan and let it cool completely before slicing into 12 equal pieces.
Optional Glaze: If desired, make a glaze by whisking together 1/2 cup (60g) of powdered sugar and 2-3 tablespoons (30-45ml) of milk until smooth. Drizzle over the cooled cake before serving.