Preheat oven to 325 degrees F. Line an 8 inch glass pan with strips of parchment paper.Melt the butter in a small saucepan over medium heat.
Heat over medium, swirling pan often, just until the butter starts to turn brown.
Remove from heat and stir in the brown and white sugar.
Let cool for about five minutes.Meanwhile, mix together the flour, baking powder, baking soda and salt.
Add the cold egg and the yolk to the sugar mixture and stir well. Stir in the corn syrup and vanilla until well blended. Stir in the flour, then stir in the walnuts. Scrape batter into the pan, spreading to the edges.
Bake 25 to 35 minutes (see note) in the glass dish or until top is golden brown and toothpick inserted in center comes out clean. Cool completely and chill slightly before cutting into squares.Top with a scoop of vanilla ice cream and some Root Beer Magic Shell.