Trim the ends of the limes and cut into wedges. Wash well to remove any wax or residue on the skin.
In a blender, combine half the lime wedges, half the sugar, half the water, and half the ice. Pulse 4–6 short bursts (3–4 seconds each) to release juice without bitterness. Repeat with remaining ingredients.
Pour the blended mixture through a fine-mesh strainer into a pitcher, pressing gently to extract liquid. Discard solids. Stir in the sweetened condensed milk until fully combined.
Taste and add more sugar or water if needed. Add fresh ice, garnish with lime slices or mint, and serve immediately.
Notes
Pulse the blender—over-blending the peel creates bitterness.
For a lighter version, substitute half the condensed milk with evaporated milk and reduce sugar.
To make a frozen slush, use frozen lime wedges instead of ice and blend a bit longer.