Mix cold water and sugar. Chill until ready to use.
Wash limes thoroughly. Cut off ends and then cut each lime into eighths.
Place half the limes and half the water/sugar mixture in a blender. Pulse 5x. Strain into pitcher with a fine mesh sieve. Dump pulp in trash. Repeat with other half of limes and water/sugar mixture.
Add ice and condensed milk right before serving. Stir and enjoy.