Special equipment: mini-muffin pan, 6 drinking straws
For the cupcakes: Place a rack in the center of the oven and preheat the oven to 350 degrees F. Line a mini-muffin pan with cupcake liners. In a large bowl, sift together the cocoa powder, flour, sugar, baking soda and salt. Add the egg, milk, water, oil and vanilla and mix with a wooden spoon or spatula until the batter is smooth. Divide the batter equally into the mini-muffin cups, filling each cup about 2/3 full. Bake until a toothpick inserted into the center of a cupcake comes out clean, with no crumbs attached, about 18 minutes. Transfer the cupcakes to a wire rack and cool completely.
For the whipped cream: In the bowl of an electric mixer, combine the heavy cream, mascarpone, powdered sugar and vanilla. Whip until the cream has soft peaks, about 2 minutes. Transfer 1/4 cup of the whipped cream into a piping bag and frost 6 of the cupcakes. Decorate the cupcakes with some of the sprinkles. Place the frosted cupcakes in the freezer and chill the rest of the whipped cream in the refrigerator while you make the shakes.
For the shakes: In a blender, combine the ice cream, milk and cocoa powder and blend until smooth. Add the unfrosted cupcakes and pulse a few times to incorporate, then puree until the cupcakes are mixed well throughout. Pour the milkshakes into 6 glasses and top each with a dollop of whipped cream and a few more sprinkles. Push a straw through each frosted mini cupcake and insert the straws into the shakes.