Position rack at center of oven and preheat to 375 degrees F.
Generously butter the twelve indentations of a madeleine mold pan (where each shell is 3-by-2-inches). Lightly dust the indentations with flour and remove the excess.
In the top of a double boiler set over hot, not simmering, water, melt the chocolate, stirring frequently until smooth. Remove the top of the double boiler containing the chocolate and set aside to cool for 5 to 10 minutes.
In a small bowl, stir together the flour, baking powder, and salt.
In a medium bowl, using a hand-held electric mixer set at med-high, beat the butter and the sugar together for 30-60 seconds, until creamy.
Add the egg yolk and continue mixing for 20-30 seconds, until light.
Beat in the melted chocolate.
Reduce the speed to low and mix in the milk and vanilla.
Add the flour mixture and mix just until smooth.
In a medium bowl, using a hand-held electric mixer set at low speed, beat the egg white until frothy. Gradually increase the speed to medium-high and continue beating the egg white, until stiff, shiny peaks form when the beaters are lifted. Fold the egg white into the chocolate mixture, until evenly mixed.
Divide the batter between the buttered molds. Smooth the tops so that the batter is level with the top of each mold.
Bake the madeleines for 12 to 15 minutes, until they spring back when gently pressed with a finger. Do not overbake, otherwise the madeleines will lose their moist, almost fudgy texture.
Cool the madeleines in the pan on a wire rack for 10 minutes.
Unmold the madeleines by inverting the pan onto a work surface and gently tapping.
Serve them warm, or cool completely and store in an airtight container.