1. **Prep Limes:** Wash the limes thoroughly under warm water and scrub them with a vegetable brush or sponge to remove any wax or pesticides from the skin. Cut the ends off the limes, then slice them into quarters or eighths.

2. **First Blend (Juice):** Place the lime wedges, cold water, and sugar into a high-powered blender. Pulse 5 to 10 times, or blend continuously for *no more than 10 seconds*. **Crucial Step:** Do not over-blend! If you blend too long, the white pith will release too much bitterness.

3. **Strain:** Place a fine-mesh sieve over a large pitcher or bowl. Pour the blended mixture through the sieve to strain out the rinds and pulp. Use a spoon to press down on the pulp to extract as much juice as possible. Discard the solids.

4. **Second Blend (Creamy):** Rinse out your blender quickly. Pour the strained lime juice back into the blender. Add the sweetened condensed milk and the ice cubes.

5. **Finish:** Blend on high speed until the ice is crushed and the drink is frothy and white (about 30 seconds).

6. **Serve:** Pour immediately into tall glasses. Garnish with a lime wheel and an extra drizzle of condensed milk on top if desired.