Wash the limes well under cool running water.
Trim off the hard ends, then cut each lime into quarters.
Add the quartered limes, cold water, and sugar to a blender.
Blend for only 5 to 10 seconds. The limes should look broken up, not fully pureed.
Pour the mixture through a fine mesh strainer into a pitcher.
Press the pulp gently, then discard the solids.
Pour the strained lime mixture back into the blender.
Add the sweetened condensed milk and ice.
Blend for 10 to 15 seconds, just until creamy and frothy.
Taste and adjust with more sugar, condensed milk, or lime juice if needed.
Serve immediately over fresh ice.