Thoroughly scrub the exterior of the 4 limes under cold water with a vegetable brush to remove any residual wax coatings or impurities. Pat completely dry.
Trim off and discard the dark stem ends and blossom tips of each lime. Cut each fruit lengthwise into 8 uniform wedges, then slice out the white central core tissue from each piece to minimize bitterness.
Place the prepped lime wedges into a high-powered blender and add the 4 cups of filtered ice-cold water.
Secure the blender lid tightly and blend on high speed for exactly 15 to 20 seconds until the fruit is broken down but not completely pulverized.
Pour the mixture immediately through a fine-mesh strainer into a clean pitcher, using a silicone spatula to gently press out all the liquid. Discard the leftover solids immediately.
Rinse the blender container to remove any remaining pulp bits, then pour the strained lime liquid back into the jar.
Add the 1 can of sweetened condensed milk to the liquid base.
Blend on medium-high speed for 10 to 15 seconds until completely smooth, thoroughly emulsified, and frothy.
Divide the solid ice cubes among 4 pre-chilled glasses, pour the fresh drink over the top, and serve immediately.