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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.

Summary:
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.