Preheat the oven to 400 degrees F. Brush a popover pan (or a muffin pan) with 2 tablespoons of the brown butter.
Add the eggs to a blender and puree until combined. Add in the warmed milk, the vanilla, remaining butter, flour and salt, blending until the batter is combined.
Place the pan in the oven and heat it for 5 minutes. Remove it from the oven and pour the popover batter in the pan, filling the tins 3/4 of the way full. Add half of the chopped chocolate to the tins. Bake for 25 to 30 minutes and do NOT open the oven!
Once the popovers are finished, remove them from the oven and sprinkle with the remaining chocolate. Let cool slightly before serving with whipped cream.