Prepare peppermint cream first: Place cream, finely crushed peppermint, and powdered sugar in bowl of electric mixer and whip just to stiff peaks. Using a pastry bag with a large tip, pipe dollops onto a parchment-lined baking sheet, making approximately 6-8. (Mixture can also be spooned on instead of piped.) Sprinkle each dollop with some of the coarsely crushed peppermint. Place in freezer for about a half hour or until firm.

For hot cocoa: Whisk together cocoa powder, sugar, and salt in a saucepan. Add hot water and bring to a boil over medium-high heat. Boil for 2 minutes; add milk, and heat but do not boil. Pour into mugs and top each serving with a dollop of the frozen peppermint cream. Serve immediately.