1. Bring water and dates just to a boil in a 1-quart heavy saucepan, then transfer mixture to a food processor and add cocoa powder and chocolate, pulsing once to combine.
2. Let cool 2 minutes, then add brown sugar, egg, vanilla, baking soda, and a pinch of salt, then purée until smooth. Add flour and pulse just until incorporated.
3. Spray mini muffin cups with cooking spray. If pan is not nonstick, line sprayed bottoms with rounds of wax paper, then spray paper.
4. Spoon batter into cups, dividing it evenly, and bake in middle of oven until a wooden pick or skewer comes out clean, 18 to 22 minutes. Cool cupcakes in pan on a rack 10 minutes, then turn out onto rack (remove wax paper, if using) and cool completely, right side up.
5. While cakes cool make frosting. Place butter, milk, vanilla, food coloring, and 2 cups of the confectioners' sugar in a mixing bowl. Beat on medium speed until smooth and creamy. Gradually add remaining sugar until light and fluffy.
6. Ice tops of cupcakes with pink frosting. Serve on a beautiful tray or tiered cake plate.

Makes 12 cupcakes.

Make ahead: cupcakes can be made and cooled (but not dusted with sugar) 1 day ahead and kept in an airtight container at room temperature.