Preheat the oven to 180 degrees. Keep a square baking pan ready.
Chop the bread into pieces with or without the side. Spread into the pan.
Beat the egg yolks well, then add the milk and beat well. Warm this mixture on low flame till just hot.
Put the 1/3 cup sugar in a thick saucepan and allow it to caramelize on low flame.
As it melts and turns amber color, add in the butter and mix well till it melts.
Pour this slowly into the egg milk mixture and whisk till combined. Pour this mixture onto the bread and allow it to soak up the milk.
Beat the egg whites till stiff. Add in the 2 tbsp sugar and beat again.
Spread over the bread and slowly fold in using a spoon.
Bake for 40 minutest till browned. Serve warm.