Cut lemons and limes in half and juice them thoroughly using a citrus juicer or by hand.

Pour the citrus juice through a fine-mesh strainer into a bowl to remove any pulp or seeds.

Transfer the strained lemon and lime juice into a large pitcher.

Pour the simple syrup into the pitcher with the citrus juice and stir to combine.

Chill the pitcher in the refrigerator for at least 30 minutes or until the mixture is thoroughly chilled.

Remove the pitcher from the refrigerator and pour in the chilled sparkling water, stirring gently to preserve carbonation.

Divide the ice cubes among four tall glasses, filling each glass about halfway.

Pour the cooler mixture over the ice, dividing it evenly among glasses. Top each glass with a sprig of fresh mint if desired and serve immediately.