Grate the Chocolate

In a food processor, process the chocolate until very fine.

Make the Caramel

Use a medium heavy saucepan, preferably nonstick, with a pouring lip. Alternatively, have ready a 2-cup heatproof glass measure, coated lightly with nonstick cooking spray.

In the saucepan, stir together the sugar and water until all the sugar is moistened. Heat on medium-high, stirring constantly, until the sugar dissolves and the syrup is bubbling. Stop stirring completely and allow the syrup to boil undisturbed until it turns deep amber. An instant-read thermometer will register 370°F/188°C or a few degrees lower because its temperature will continue to rise. Remove it from the heat and, as soon as it reaches temperature, slowly and carefully pour the hot cream into the caramel. It will bubble up furiously.

Use a silicone spatula or wooden spoon to stir the mixture gently, scraping the thicker part that settles on the bottom. Return the pan to very low heat, continuing to stir gently for 1 minute, or until the mixture is uniform in color and the caramel is fully dissolved. Remove it from the heat and gently stir in the butter until incorporated. If the saucepan doesn’t have a pouring lip, pour the mixture into the glass measure.

Add the Caramel to the Chocolate

With the motor of the food processor running, pour the hot caramel sauce onto the grated chocolate. (The caramel will be between 160° and 200°F/71° and 93°C when added to the chocolate. If the caramel should harden in the glass measure, simply put it in the microwave for a few seconds to soften it.) By the time all of it is added, the chocolate will have melted and the mixture will be smooth and shiny. Add the vanilla and pulse it a few times until evenly combined.

Using a silicone spatula, scrape the ganache into a bowl, allow it to stand uncovered for 1 hour, then cover it with plastic wrap and allow it to sit at room temperature for about 2 hours, or until firm enough to spread as filling and frosting. It should be the creamy consistency of softened butter.