For the Cupcakes:
Line muffin cups with paper liners
Place an oven rack in the center of the oven and preheat to 325 degrees F.
Combine the unsweetened chocolate and water in a small saucepan over medium-low heat. Stir constantly until the chocolate is melted, about 2 minutes. Cool for 2 minutes. Whisk in the mascarpone cheese until the mixture is smooth.
Beat the sugar, oil, eggs, and vanilla in a large bowl for 30 seconds. Stir in the mascarpone mixture. Whisk the flour, baking soda, salt, baking powder, and chocolate chips in a medium bowl. Add the dry ingredients to the chocolate mixture. Stir until just blended.
Divide the batter among the prepared muffin pans. Bake for 20 to 25 minutes or until a tester inserted into the center of a cupcake comes out with no crumbs attached. Cool the cupcakes completely before dipping, about 1 hour.
For the Ganache:
Place the chocolate chips in a small bowl. Combine the heavy cream and vanilla extract in a small saucepan over medium-low heat. Cook until small bubbles appear on the outside edge of the cream. Pour the hot cream mixture over the chocolate chips. Using a fork, gently stir until all the chocolate is melted and the mixture is smooth.
Dip the tops of each cupcake in the ganache and transfer to a baking sheet. Place the dipped cupcakes in the refrigerator to set, about 15 to 20 minutes. Allow cupcakes to return to room temperature before serving.
Cook's Note: For puffier cupcakes allow the batter to rest in the muffin pans for 20 minutes before baking.