In a blender, combine 4 ounces dark chocolate, chopped, and 1/4 cup sweetened cocoa (not instant). In a 1- to 2-quart pan over medium-high heat, bring 1/2 cup whole milk to a boil; pour milk over chocolate mixture and whirl until melted and smooth.
Pour in 1 1/2 cups cold half-and-half and whirl to blend.
Place 1 cup ice cubes in a cocktail shaker and add half of the chocolate mixture. Shake until cold and strain into a 16-ounce glass with a few ice cubes in it.
Fill glass with club soda and stir. Garnish with whipped cream and/or shaved chocolate.