Chop 3-4 ripe fuzzy peaches and add them to a medium saucepan along with 1 cup of filtered water and ¾ cup of granulated sugar. Mix gently to coat peaches in sugar.

Place the saucepan over medium heat and let the mixture come to a gentle simmer, stirring regularly for about 5 minutes until sugar dissolves.

Simmer the mixture for 10-15 minutes or until peaches are soft and break apart easily. Adjust heat to prevent burning.

Remove from heat and mash the peaches in the saucepan to release more juices.

For smoother syrup, strain the mixture using a fine-mesh sieve over a bowl. Press down on solids to extract syrup, discarding solids.

Cool the strained peach syrup completely at room temperature for about 15-20 minutes or in the refrigerator.

In a blender, combine the cooled peach syrup with the juice of 2 fresh limes and 2 cups of ice cubes. Blend until smooth and frosty.

Taste your drink and adjust sweetness or acidity as desired. Blend again if you've made adjustments.

Pour the drink into colorful glasses and garnish with mint sprigs and peach slices if desired.

Top each glass with a splash of sparkling water or club soda just before serving.