Place unsalted butter in a medium saucepan, then cook over medium heat, stirring occasionally, until the butter turns foamy and is a deep golden brown color. Cool.
In a large bowl, whisk together brown sugar, maple syrup, and eggs until very well mixed. Pour in the melted browned butter, then mix again.
Add all-purpose flour, Kosher salt, baking powder, then use a spatula to fold until just a few streaks of flour remain.
Transfer to the prepared pan, then smooth into a flat even layer. Sprinkle with the remaining white chocolate chips and chopped walnuts, then bake until the edges are fully set and golden brown, but the center still jiggles slightly. Remove from the oven, sprinkle lightly with flaky sea salt, then cool on a wire rack.
Place unsalted butter in a saucepan over medium heat. Once melted, add maple syrup. Stir well. Remove from the heat, then add 1 tsp vanilla extract, confectioners’ sugar, and a generous pinch of Kosher salt. Stir until very smooth. Taste, then add additional sugar if you want it sweeter.