To prepare the blondies, preheat oven to 350º F. Melt butter in a medium saucepan over moderate heat. Once the butter has melted, add brown sugar and salt, stirring to combine. Continue cooking until the mixture just begins to boil. Remove from heat and cool slightly.
In the meantime, generously butter an 8-inch square metal baking pan. Add a layer of parchment paper, leaving the edges long enough to lift the blondies from the pan once cool for easier slicing. Butter the parchment paper, pressing it down to help it adhere smoothly to the pan. Set aside.
Mash banana in a medium-sized bowl. Add egg and vanilla, mixing well to combine.
Add banana mixture to the pan with the brown sugar mixture, stirring until well combined. Mix in flour until combined. Fold in chocolate chunks.
Spread batter into the prepared pan.
Bake for 25-30 minutes until center is set. Transfer pan to wire rack to cool
When the blondies come out of the oven, begin making frosting. Melt butter in a medium saucepan. Add brown sugar, salt, and milk. It will bubble up a bit; stir carefully until smooth and well combined. Continue cooking until the mixture just comes to a boil. Remove from heat and let cool for 5 minutes.
Whisk powdered sugar into the pan and then spread frosting on top of the blondies. Set aside to cool completely.
Once cool, add the chocolate glaze. Melt bittersweet chocolate and butter in short bursts in the microwave. Once melted, stir until smooth and glossy. Mix in vanilla extract. Drizzle glaze over the frosted blondies.
Once the glaze has set, lift the blondies from pan using the parchment paper and slice into squares.