1. Start by mixing 1 cup of granulated sugar with 6 cups of cold water to create a simple syrup, then chill it until ready to use.
2. Wash the limes thoroughly with soap, cut off the ends, and slice each into eighths.
3. Place half of the lime pieces and half of the sugar water into a blender, then pulse the mixture about five times or for no more than 15 seconds to avoid bitterness.
4. Strain the blended mixture through a fine mesh strainer into a pitcher, pressing the pulp with a spoon to extract all the juice; discard the solids.
5. Repeat the process with the remaining limes and sugar water.
6. Add 6 tablespoons (or 1/2 cup for variation) of sweetened condensed milk to the pitcher and stir well.
7. Adjust with extra sugar or milk if needed for desired sweetness and creaminess.
8. Serve immediately over ice, adding ice to individual glasses rather than the pitcher to prevent dilution.
9. Garnish with fresh lime slices if desired.