Wash and soak the uncooked rice for 3-4 hours, then drain off the water. Grind the uncooked rice and cooked rice together in a blender to form a fine paste, adding a little of the coconut milk. Once it is ground to a fine paste, remove it from the grinder; add the sugar, the remaining coconut milk and salt to taste. Mix the yeast with a little warm water, and add to the rice paste. Mix well and make sure the batter is smooth and of dropping consistency. If it's a bit stiff, add 2 tablespoons of milk to make it liquid enough. Cover and set aside in a warm environment for a further 2 to 3 hours.
Lightly grease a deep non-stick pan with oil or fat, place over a medium heat and, when the pan is hot, pour in one big ladle of the batter. Slowly rotate the batter on the pan so that a thin layer forms on the side while the middle remains thick. Cover with a lid and cook for about one minute until the middle becomes fluffy and the edges turn golden. Keep the appam warm then repeat the same with the remaining batter. Transfer the appams to a plate and serve them hot with chicken curry, vegetable korma or a spicy stew.