1. In a heavy 2- to 3-quart saucepan, combine the sugar and water and cook over moderate heat, stirring only until the sugar dissolves.
2. Cook undisturbed until the syrup reaches a temperature of 230° on a candy thermometer, or a small amount dropped into ice water immediately hardens into a thread.
3. In a small bowl, quickly mix the egg yolks and flour together until they are well blended, then add 2 tablespoons of hot syrup, stirring constantly. Slowly pour the mixture into the syrup in the saucepan, stirring constantly.
4. Add the coconut and simmer over low heat, stirring, until the mixture becomes very thick and stiff. Do not allow the mixture to come to a boil at any point.
5. Remove the pan from the heat, stir in the vanilla, and let the mixture cool to room temperature. Preheat the oven to 375°. Shape the cookie mixture, a tablespoon at a time, into small balls by rolling it quickly between your palms.
6. Arrange the balls 1 inch apart on a buttered cookie sheet and bake in the center of the oven for 15 minutes, or until the cookies are a delicate golden brown. Cool and serve.
