Combine the ingredients in a blender and 3whir on high speed until the mixture is thoroughly pureed.
With the blender running, slowly add more ice cubes, no more than three at a time. Listen carefully to the sound of the machine. When the machine resumes its normal pitch rather than sounding gravelly, look at the drink. You will notice a vortex in the center of the mixture. Keep adding ice until the vortex disappears and the mixture looks smooth.
Turn off the blender and stir the mixture with a long spoon or a chopstick. Replace the lid and turn on the blender. The vortex will reappear. Keep adding ice cubes, two or three at a time, until it disappears.