In a large bowl, whisk together the pudding mix and 3 cups milk until smooth and well combined. Stir in the chopped chocolate. In another medium bowl, whisk to combine Cool Whip with 1/4 cup milk. In another small bowl, whisk to combine cherry preserves and 2 tablespoons water.
Spoon a tablespoon of the pudding into each popsicle mold and top with a spoonful of whipped topping. Pour the pudding mixture halfway up the molds and add a spoonful of preserves. Top off each with remaining pudding, insert popsicle sticks and freeze until firm, at least 6 hours or overnight.
Unmold and garnish with shaved chocolate and fresh cherries.