In a large mixing bowl, combine cold, filtered water with granulated sugar. Stir until the sugar is fully dissolved. Cover and chill in the refrigerator.

Wash the limes under running water, cut off the ends, and slice them into eighths. Set aside.

In a blender, combine half of the lime pieces with half of the chilled sugar water mixture. Blend on pulse for about 5 seconds.

Pour the lime mixture through a fine mesh sieve into a pitcher. Press down on the solids to extract as much liquid as possible.

Repeat blending with remaining lime pieces and sugar water mixture. Strain again.

Fill the pitcher with ice and stir in sweetened condensed milk. Mix until combined.

Pour into chilled glasses, garnish with fresh lime slices and mint leaves if desired, and serve immediately.