Heat oven to 350 degrees F.
Heat 1 cup of sugar, slowly, in a heavy skillet, stirring constantly with a wooden spoon until sugar melts and is free of lumps. When the sugar turns a caramel color, remove it from the heat and pour it into a 6-cup mold. Set aside.
Beat the eggs with 2 cups sugar, until fluffy. Place flour in a small bowl and add 2 tablespoons coconut milk, one at a time until mixture is smooth. Add the flour mixture to the coconut milk, mix well and then add to the egg mixture. Pour mixture over into mold over caramelized sugar. Place the mold in a large baking pan filled with 1 inch of hot water to create a bain-marie. Bake for 40 minutes. Remove from water bath immediately. Cool for 20 minutes then invert onto a serving dish and chill for 6 to 8 hours. To serve, sprinkle with freshly grated coconut if desired.
Cook's Note: Instead of grating a fresh coconut I have used frozen fresh coconut found the freezer department of most supermarkets. It works just as well.