Heat the oven to 350°. Line a large baking sheet with parchment paper or a silicone baking mat. Or grease the baking sheet.
In a mixing bowl combine the flour, butter, beaten whole egg, 1/2 cup of the granulated sugar, 1 1/2 cups of the coconut, and almond or vanilla extract. Beat until a soft dough is formed.
Shape the dough into 1-inch balls.
Roll each ball in the egg white mixture then in the remaining 1 1/2 cups of coconut.
Arrange on the baking sheets, leaving about 1 1/2 to 2 inches between them.
Dip the flat bottom of a cup or glass in the remaining 3 tablespoons of sugar and press the cookies to flatten to about 1/3-inch in thickness.
Bake the cookies for 10 to 12 minutes, or until set and golden brown on the bottoms.
Makes About 2 to 2 1/2 Dozen