Preheat the oven to 350F. Grease and line a standard (9x5”) loaf pan with parchment paper so some hangs over the sides.
Add the ½ cup (113g) of butter to a saucepan over medium-high heat. Allow to melt and brown, while stirring continuously (~5-8 minutes).
Once the brown butter reaches a deep golden amber color and smells nutty, remove from the heat and immediately pour into a large bowl. Set aside to cool slightly (about 15-20 minutes).
Prepare the brownie batter filling by combining the butter and chocolate chips in a small bowl. Melt them together in the microwave at 20-second intervals, stirring between each, until smooth. Whisk in the cocoa powder and instant espresso powder (if using). Set aside to cool slightly.
In a separate medium bowl, add the egg, both sugars, and vanilla. Whisk together until well combined and frothy.
Once the chocolate mixture is slightly cooled, add it into the egg/sugar mixture and whisk to combine.
Fold in the flour and salt, then fold in the chocolate chips. Set the brownie batter aside.
Prepare the banana bread batter by whisking together the flour, baking soda, baking powder, and salt in a separate medium bowl.
To the bowl with the cooled brown butter, add the mashed bananas, brown sugar, Greek yogurt (or sour cream), eggs, and vanilla. Whisk until well combined.
Add the dry ingredients to the wet and mix until just combined, being careful not to over-mix. Gently fold in the chocolate chips.
Pour half of the banana bread batter into the prepared loaf pan and spread out evenly. Create a divot in the middle for the brownie batter.
Scoop the brownie batter filling into the middle of the banana bread batter and spread it into an even layer.
Top with the remaining banana bread batter and spread it evenly to cover the brownie batter filling.
Run a butter knife or toothpick down the center of the batter lengthwise. Optionally, place two thin strips of cold butter in the crease.
Bake at 350F for 70-75 minutes, until golden brown and a toothpick inserted comes out clean or with a few moist crumbs.
Remove from the oven and let cool in the pan for at least 15-20 minutes before transferring to a wire cooling rack. Allow to cool for at least another 45-60 minutes before slicing.
