Wash the limes thoroughly under cool water and cut each lime into quarters.

Blend the quartered limes with 4 cups of fresh water on high for about 1 minute.

Strain the mixture through a fine mesh sieve into a large bowl, pressing down on the pulp.

Return the strained lime juice to the blender, add 2 more cups of water, sugar, and sweetened condensed milk, then blend on low for 1 minute.

Skim off any frothy foam, pour over ice-filled glasses, and garnish with lime wedges.