While the shortbread is baking, make the filling. First, add the white and brown sugar to a large heatproof bowl. Set aside. Next, brown the butter. Melt the butter in a light colored saucepan or skillet (using a light color vs nonstick makes it easier to see the color of the butter as it browns). Melt the butter over medium heat, stirring frequently until the butter turns an amber and golden brown bits form at the bottom. About 5 minutes. Be careful, it will go from brown to burnt very quickly. Remove from heat and pour over the sugar. Stir together.