Frozen Hot Chocolate

Break the bittersweet chocolate into pieces and place it in a medium bowl set over a pot of simmering water, stirring occasionally, until just melted. Off the heat, whisk in the cocoa powder, sugar, and half-and-half and set aside

Place ¾ cup of the milk, 2 tablespoons of the coffee liqueur, ½ teaspoon of the vanilla, and half of the chocolate mixture in a blender. Add 2 cups of the ice and blend for several minutes, until the mixture is thick but not icy, like a frozen daiquiri. (You can add a little more milk or ice if it’s too thick or too thin.) Pour into two (10-ounce) ice cream soda glasses and top each with a generous dollop of whipped cream and some grated chocolate. Repeat for the second two glasses. Serve ice cold with straws and long-handled spoons.