Heat oven to 350 degrees. Mix coconut, cornstarch, sugar, egg whites, and vanilla in heat-proof bowl. Set bowl over a pot of boiling water (or use a double boiler). Heat, stirring until the mixture thickens, about 4 minutes. Remove from heat and set aside. Spoon out macaroons, about a scant tablespoonful each, and place on ungreased baking sheet. Bake at 350 for 10-15 minutes or until lightly golden but still soft and chewy. Remove to a wire rack to cool.
Place chocolate in a small microwave-safe bowl and heat on HIGH power for 1 minute. Stir until smooth, microwaving more if needed. Dip bottoms of cookies in chocolate, allowing excess to drip back into bowl. Place on a waxed paper-lined baking sheet in refrigerator to set.