Rinse rice thoroughly under running water. Cover and soak for at least 2 hours, but it is better to soak overnight.
Drain rice, but reserve 1½ to 2 cups of the liquid.
In a blender or food processor grind the rice as finely as possible. Add some of the soaking liquid if necessary.
Add cinnamon, ginger, vanilla extract and the zest of the lime and continue grinding. Add the rest of the water and milks until everything is well blended.
Transfer to a saucepan and add the egg yolks. Turn heat on to medium low and whisk constantly until the temperature of the mixture reaches around 115ºF or when you can still touch it with your finger but not for long.
Refrigerate for at least 2 hours before transferring to the ice cream machine.
Recipe by What's Cooking, Mexico? at http://whatscookingmexico.com/2008/08/26/more-ice-cream/