Assemble and freeze the parfaits up to a day ahead; to serve, dollop with whipped topping and sprinkle with cinnamon. You can place the parfait glasses in the freezer about 30 minutes before assembling to help the layers firm up quickly.
Combine ice cream and coffee granules, stirring until coffee granules dissolve. Spoon 1/4 cup ice cream mixture into each of 6 (8-ounce) parfait glasses. Drizzle each serving with 1 teaspoon brewed coffee. Repeat layers, ending with ice cream mixture. Cover and freeze until firm. Just before serving, top each parfait with 1 tablespoon whipped topping and 1/8 teaspoon cinnamon.