Preheat oven to 300 degrees F (150 degrees C). Line 2 baking sheets with parchment paper.

In a medium bowl, beat the egg whites until stiff but not dry. Fold in cornstarch. Transfer to the top of a double boiler and set over low heat.

Stir in sugar and cook for about 3 to 4 minutes, until edges of mixture begin to pull away from pan. Remove from heat and stir in vanilla extract. Stir in coconut.

Drop dough by spoonfuls 1 1/2 inches apart on the prepared baking sheets. Bake for 20 to 25 minutes until golden brown and firm to the touch. Cool on the pans on wire racks.