Wash the limes under running water, cut off the ends, and slice each into eighths.

In a blender, combine half of the lime pieces, half of the sugar, and half of the cold water. Blend until combined.

Pour the blended mixture through a fine-mesh sieve into a pitcher, pressing out as much juice as possible. Repeat with remaining ingredients.

Add sweetened condensed milk to the strained lime juice and whisk until fully blended.

Serve over ice and garnish with lime wedges or mint.