Heat oven to 350 degrees F.
Mix coconut, cornstarch, sugar, egg whites and vanilla extract in heatproof bowl (or a double boiler).
Set bowl over a pot of boiling water. Heat for 4 minutes, stirring often. Remove from heat and set aside.
Spoon out coconut mixture by the tablespoonful, and place on an ungreased baking sheet.
Bake at 350 degrees for about 15 minutes or until lightly golden but still soft. Remove immediately to a wire rack to cool.
Place chocolate and vegetable shortening in a small microwave-safe bowl and heat for 1 minute and 15 seconds. Stir until smooth, microwaving in 15- second increments if needed.
Place one cookie on a fork and gently press 1 to 2 almonds on top, so they adhere to the cookie. Holding the fork over the bowl of chocolate, carefully spoon chocolate over top, allowing excess to drip back into bowl. Place cookie on a rack over a waxed or parchment paper lined baking sheet. Repeat with remaining cookies. Place rack in refrigerator for chocolate to set, at least 20 minutes. Makes 2-1/2 dozen cookies.