In a blender, combine the quartered limes and granulated sugar. Pulse a few times until the limes are roughly chopped.

Add the cold water to the blender and blend on high for about 30 seconds.

Strain the mixture through a fine mesh sieve or cheesecloth into a pitcher to remove the pulp and seeds.

Stir in the sweetened condensed milk until well combined.

Serve over ice cubes and garnish with lime slices if desired.