Preheat oven to 350°F. Grease a 13- x 9-inch baking pan with cooking spray; line using parchment paper, leaving a 1-inch overhang on 2 long sides.

Melt butter in a medium saucepan over medium until foamy and bubbling. Cook, swirling butter and stirring often, until butter is golden brown and has a nutty fragrance, 2 to 3 minutes more. Transfer to a large heatproof bowl; whisk in brown sugar and granulated sugar until well combined, about 1 minute. Set aside until cool to the touch, about 5 minutes. Whisk in mashed bananas and eggs.

Whisk together flour, salt, baking powder, and cinnamon in a medium bowl. Add to butter mixture in large bowl, and stir until just combined; gently stir in walnuts.

Pour batter into prepared baking pan, and spread evenly to edges.

Bake in preheated oven until starting to brown on top and a wooden pick inserted into center comes out with a few moist crumbs attached, 22 to 25 minutes. Cool completely in baking pan on a wire rack, about 2 hours.

Stir together brown sugar, butter, and milk in a medium saucepan. Bring to a boil over medium, stirring often; cook for 2 minutes. Remove from heat, and let cool about 5 minutes. Whisk in powdered sugar until smooth. If needed, stir in additional milk, 1 teaspoon at a time, until smooth and spreadable.

Spread evenly over cooled Brownies. Remove Brownies from baking pan using parchment overhang as handles, and transfer to a cutting board. Garnish with additional chopped walnuts; cut into 12 pieces.