Stir together coffee, sugar, and 1 tablespoon milk in a small glass measuring cup. Pour into ice cube trays, and freeze at least 2 hours or until firm.
Process coffee ice cubes, 1 1/4 cups milk, and chocolate syrup in a blender until smooth. Dollop evenly with whipped topping, and sprinkle with chocolate shavings. Serve immediately.
Note: To make strong brewed coffee, use 3 tablespoons coffee grounds to 1 cup water.
