Place a double boiler over medium heat. Add both cocoa powders, the sugar and butter. Whisk until cocoas and sugar have melted and creamed together with the butter. Add a little of the milk. Add chocolates, whisking as they melt. Slowly pour in additional milk, reserving one cup milk for next step. Whisk until mixture is smooth. Remove from heat and let cool to room temperature.
In a blender, make three servings at a time. Add 1/2 cup chocolate base, 1/2 cup milk and about 2 cups crushed ice. Blend until smooth, adding more ice or liquid as needed to reach a perfect texture. Repeat with remaining ingredients or store any unused chocolate base in the refrigerator, covered. Pour frozen hot chocolate into large goblets and top with whipped cream and grated chocolate. Serve immediately with a straw and a long spoon.
Author and food stylist Fred Thompson says he didn't like waiting in line for the famous frozen hot chocolate at Serendipity 3 in New York City, so he decided to create his own recipe, featured in his book Hot Chocolate (Harvard Common Press, 2006). "Serendipity has published its 'secret recipe,' but you need a trip to Europe to buy all the chocolates," says Thompson, who divides his time between NYC and Raleigh, N.C. "My version makes shopping easier." Thompson recommends double-batching the base and storing it in the refrigerator. "I have yet to see the time when one was enough," he says.
Recipe from Hot Chocolate (Harvard Common Press, 2006) by Fred Thompson, photographer Brian Hagiwara