Preheat oven to 400 (200 C) degrees. If you're baking in a convection oven, set the temperature to 375 (190 C) degrees. Brush (6) 4-ounce ramekins or custard cups with the melted butter. Arrange them in a baking dish.
Add a few inches of water to a medium saucepan and bring to a simmer. Put the chocolate and 4 tablespoons butter in a medium heatproof bowl. Set the bowl over the saucepan (adjust the temperature to low so the water doesn't boil).
When the butter and chocolate start to melt, remove the bowl from the heat, using a towel or oven mitts to protect your hands. Stir until the mixture is completely melted and smooth.
Beat the sugars, eggs, vanilla and salt in an electric mixer fitted with the paddle attachment until pale and thickened, about 5 minutes at medium-high speed. Lower the mixer speed and add the flour, stirring until just combined. Pour in the chocolate mixture and stir until blended and smooth, about 1 minute.
Spoon the batter evenly into the ramekins. Sprinkle some nibs over each one. Pour enough water into the baking dish so that it comes halfway up the sides of the cups.
Bake 15-17 minutes, or until the cakes are puffed on top and a toothpick inserted into the center comes out coated with moist batter. Let them cool for 2 minutes, then carefully remove the cups and set them on a rack to cool for 5 minutes. Serve the budino cakes warm, with whipped cream spooned on top.
To quickly bring eggs to room temperature, crack them into a small bowl while you assemble the rest of the ingredients for the recipe.
If you don't have cacao nibs, shave some chocolate over the whipped cream when serving or top the cakes with mini chocolate chips or finely chopped nuts (almonds, walnuts or hazelnuts)
You can make the batter and fill the cups up to 3-4 hours before serving. Refrigerate them until you're ready to bake. This will make it easier to serve a warm dessert if you're having people over.
The baked cakes will keep 1-2 days at room temperature.