While the shortbread is baking, make the filling. First, brown he 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 very 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 stir in the sugars and salt. Let cool for 10 minutes.