Mix cold water and sugar very well and chill until ready to use. This step can be done ahead of time.
Wash limes thoroughly with soap - you need the soap to get the wax, dirt, & pesticides off of the limes since you will be using the entire lime. Cut the off the ends of the limes; then cut each lime into 8 pieces.
Place half of the limes into your blender.
Add half of the sugar water, place the lid on your blender, & pulse 5 times. Place a strainer over your pitcher & pour the blended mixture through the strainer and into the pitcher. Use a spoon to press the rest of the liquid from the strainer into the pitcher. Discard the pump & stuff remaining in the strainer. Repeat with the remaining limes & sugar water. Add the sweetened condensed milk - it's the secret ingredient! The original recipe called for 6 tablespoons, but I liked the final product MUCH better with 1/2 cup of sweetened condensed milk. You can taste it at this point & add more if you would like. If it's bitter, add a little more milk.
Serve immediately over lots of ice. This does not keep well, so do not make this in advance (although you can cut the limes, mix the sugar water, and measure the sweetened condensed milk in advance). This serves 4 people, although people will most likely want more so you may want to double or triple the recipe accordingly if need be.