Special equipment: 2 ice cube trays
Bring 2 1/2 cups water, cocoa powder, 1/2 cup of the sugar, chocolate, vanilla and 1/8 teaspoon salt to a simmer in a medium saucepan over medium heat, whisking frequently; continue to simmer and whisk until the chocolate is completely melted, about 8 minutes. Simmer for an additional 2 minutes. Let cool to room temperature, about 25 minutes. Ladle into 2 ice cube trays, and freeze until solid, about 4 hours.
When ready to serve, whisk the cream and remaining 1 tablespoon sugar in a medium bowl until stiff peaks form.
Transfer all the ice cubes to a food processor. Let sit for 5 minutes at room temperature. Pulse the ice cubes about 20 times to break them up. Blend for 10 seconds, and then pulse a few times. Repeat this 3 or 4 times, scraping down the sides and redistributing the mixture as necessary. Initially the blended ice will break apart into crumbles that don't seem to come together. Keep blending, and it will ultimately develop into a thick, smooth, sorbetlike mixture. Scoop into mugs, and top each with a layer of marshmallows and a big dollop of whipped cream.
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