Line a square 8x8 baking pan with parchment paper and preheat the oven to 350 F/180 C.
In a small pot, whisk together the milk, sugar, flour, and egg yolk. Heat over medium-low stirring constantly until it's thick like pudding, about 5-6 minutes.
Transfer the pudding to a small bowl and stir in the butter and vanilla. Set aside.
In a medium bowl, whisk together the melted and slightly cooled butter, brown sugar, and white sugar.
Whisk in the egg yolk, vanilla, and mashed banana.
Fold in the flour, baking powder, and salt until just combined.
Pour half of the batter into the prepared pan and press the vanilla wafers into it.
Use a spoon to dot the rest of the batter over the wafers, doing the same with the vanilla pudding in the empty spots.
Use a knife or toothpick to swirl the batter and pudding together, then top it with more vanilla wafers.
Bake for 30-33 minutes, or until a toothpick inserted into the center comes out clean.
Let the brownies cool completely on a wire cooling rack before cutting into 8-9 bars and enjoy!