Preheat the oven to 350° F. Line a 9×9 inch square pan with parchment paper.In a bowl, mix the granulated sugar with the lemon zest, use your fingers to rub the zest into the sugar, releasing the lemon oil. Add the brown sugar.in a bowl, whisk the eggs for 1 minute until bubbly on top. Add the lemon sugar mix. Add the butter to a pot set over medium heat. Allow the butter to brown lightly until it smells toasted, 2-3 minutes. Remove from the heat. Whisk the the butter into the sugar and eggs until smooth and glossy. Stir in the white chocolate and vanilla.Add the flour, baking powder, and salt. Stir until combined. Spread the batter into the prepared pan. Bake for 30 minutes or until just set and crinkly on top. To make the icing. Whisk the brown butter, lemon juice, vanilla, powdered sugar, and 1 tablespoon of water until smooth. Spoon over the bars. Mix the sugar and lemon zest. Sprinkle the lemon sugar over the bars. Let the icing set for 30 minutes. Slice and enjoy! Enjoy!