To keep the drink from diluting, freeze cubes of leftover coffee and half-and-half to use in place of ice.
Bring 3 1/2 cups water and coffee to a boil in a saucepan; remove from heat, and let stand 10 minutes. Pour mixture through a fine wire-mesh strainer into a bowl, discarding coffee grounds.
Stir 2 tablespoons sugar and 3/4 teaspoon cinnamon into coffee until sugar dissolves; let cool. Stir in half-and-half and syrup; chill 2 hours. Serve over ice.