Ingredients

14 flat-bottom wafer ice-cream cones 

1 cup all-purpose flour 

1/2 teaspoon baking soda 

1/4 teaspoon salt 

3/4 cup plus 2 tablespoons milk 

5 ounces unsweetened chocolate, chopped 

12 tablespoons (1 1/2 sticks) unsalted butter 

1 1/2 cups plus 2 tablespoons sugar 

1 large egg, lightly beaten 

1 1/2 teaspoons pure vanilla extract 

1/2 cup heavy cream 

Preparation

Heat oven to 350 degrees. Stand cones on an ungreased baking sheet. In a mixing bowl, whisk together flour, baking soda, and salt; set dry ingredients aside.

Fill a medium saucepan with water and set over medium heat; bring water to a boil. Reduce heat, and let water simmer. In the metal bowl of an electric mixer, combine milk, 2 1/2 ounces chocolate, and 1 stick butter. Set bowl over simmering water, stirring occasionally, until butter and chocolate have melted. Remove bowl from heat; stir in 1 cup sugar.

Transfer bowl to mixer fitted with the paddle attachment. Add reserved dry ingredients, and beat until well combined. Add egg and 1 teaspoon vanilla; beat to combine. Pour batter into cones, filling each cone three-quarters full.

Transfer baking sheet to oven, and bake until domes form and a cake tester inserted into the center of a cupcake comes out clean, 20 to 25 minutes. Remove from oven, and transfer to a wire rack to cool completely.

Meanwhile, make the icing: Combine remaining 1/2 cup plus 2 tablespoons sugar and cream in a heavy saucepan. Set over high heat, and bring to a boil, stirring constantly. Reduce heat to medium; simmer, without stirring, 5 minutes. Remove pan from heat; add remaining 2 1/2 ounces chocolate, stirring until melted. Stir in remaining 4 tablespoons butter and 1/2 teaspoon vanilla. Chill, stirring occasionally, until icing is cool enough to spread. Using an offset spatula, spread icing over cupcake tops. Serve.