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Use approximately 1 teaspoon (5 ml) of chocolate syrup to coat the inside of the glass. After you've drizzled it, place the glass in the freezer for 1 to 2 hours to chill. This step is optional. You can leave the glass uncoated if you prefer. To mix the martini, you'll need a cocktail shaker. Add enough ice to the shaker to fill it almost all the way. You can substitute a mason jar for the cocktail shaker. Pour 1 ounce (30 ml) of peppermint schnapps, 2 ounces (60 ml) of chocolate liqueur, and 2 ounces (60 ml) of half and half over the ice. Cover the shaker, and shake the mixture vigorously for about 15 seconds to combine all of the ingredients. Place a cocktail strainer over the coated martini glass, and pour the martini through it to strain out the ice. Serve it while it's still cold.
Drizzle chocolate syrup around the inside edge of a martini glass and chill it. Fill a cocktail shaker with ice. Add the peppermint schnapps, chocolate liqueur, and cream and shake well. Strain the martini into the prepared glass and serve.