Preheat the oven to 325 degrees Fahrenheit.
Heat 1 inch of water in the bottom half of a double boiler over medium heat. Place 10 ounces semisweet chocolate, 1 cup heavy cream and 2 ounces unsweetened chocolate in the top half of the double boiler. tightly cover with plastic wrap. Allow to heat for 8 minutes. Remove from the heat and stir until smooth. Set aside until needed.
Place the eggs, sugar and vanilla extract in the bowl of an electric mixer fitted with a paddle. Beat on medium until lemon-colored and slightly thickened, about 4 minutes. Add the melted chocolate mixture and beat on medium for 15 to 20 seconds more. Add the cake flour, baking soda and chocolate chips, and beat on low for 10 seconds. Increase to medium and beat for an additional 10 seconds. Remove the bowl from the mixer. Use a rubber spatula and thoroughly combine the batter.
Evenly divide the mixture into 18 bake cups that have already been positioned into muffin tins, filling the cups to within 1/4 below the rim. Bake in the preheated oven until a toothpick inserted in the center comes out clean, about 25 to 30 minutes. Remove from the oven and allow to cool to room temperature.
Heat 1/2 cup heavy cream in a 1 1/2-quart saucepan over medium-high heat. Bring to a boil. Place 6 ounces semisweet chocolate in a stainless steel bowl. Pour the boiling cream over the chocolate and allow to stand for 5 minutes. Stir with a whisk until smooth.
One at a time, dip the top of each of Granny's cupcakes into the chocolate icing. Sprinkle the grated white chocolate over the icing on each cupcake, and refrigerate for 30 minutes to set the icing.
Allow the cupcakes to come to room temperature for 15 to 20 minutes before serving.