Make the cupcakes:

Preheat the oven to 375F. In a metal bowl set over a pan of barely simmering water melt the chocolate with the water, stirring, until the mixture is smooth and remove the bowl from the heat. In a bowl whisk the butter with the brown sugar until the mixture is blended well and whisk in the yolk and the chocolate mixture. Onto a sheet of wax paper sift together the flour, the baking powder, and the salt and add the flour mixture to the chocolate mixture in batches alternately with the milk, stirring well after each addition. Stir in the vanilla, divide the batter among 6 paper-lined 1/2-cup muffin tins, and bake the cupcakes in the middle of the oven for 18 to 20 minutes, or until a tester comes out clean. Transfer the cupcakes to a rack and let them cool.

Make the frosting while the cupcakes are baking:

In a metal bowl set over a pan of barely simmering water melt the chocolate with the butter, stirring, until the mixture is smooth and remove the bowl from the heat. Stir in the confectioners' sugar, 2 teaspoons of the milk, and the vanilla and blend the frosting well (the frosting will thicken as it stands). When the cupcakes are cool, thin the frosting to the desired consistency with the additional milk, stirring in the milk drop by drop.

Spread each cupcake with some of the frosting.

Makes 6 cupcakes.