Melt the chocolate and allow it to cool. It should still be stirrable but cool. Melt in the microwave heating in 30 second increments and stirring in between until all chocolate is melted.
Add white granulated sugar to the blender or processor and pulse until sugar is powder like and ultra fine.
In mixer cream the butter and the ultra fine sugar together. Pour in the cooled melted chocolate and mix until combined. Scrape the sides to ensure completely mixed.
Add in the vanilla extract and mix on low to combine.
Add in one egg, cold from the fridge. Mix on high speed for 5 minutes.
Scrape the sides and add the second egg, cold from the fridge. Mix for another 5 minutes on high speed. The mixture will be smooth and silky.
Spoon onto the top of the cooled brownies. Don't put on while the brownies are hot, it will melt the french silk. Smooth the top with a rubber spatula or offset spatula.
Place in refrigerator and allow to cool for at least 2 hours. Store in refrigerator covered.