Place half the shredded coconut in food processor with sugar, salt and baking powder. Process mixture until finely ground.
4 cups sweetened shredded coconut, 1 cup granulated sugar, ½ teaspoon salt, ¼ teaspoon baking powder
Add chilled butter pieces and process just until no lumps remain.
½ cup unsalted butter
Add vanilla, the whole egg and egg yolk, reserving the egg white for the coating later. Process mixture just until it becomes smooth.
2 large eggs, 1 teaspoon vanilla extract
Add flour and pulse until a crumbly dough begins to form, being careful not to overmix.
1 ½ cups all purpose flour
Place reserved egg white in shallow bowl or on a plate and use a fork or small whisk to stir smooth. Place remaining 2 cups shredded coconut in another similar container. Scoop dough using a tablespoon and shape into balls. Dip coconut cookie dough balls in egg white. Then roll in shredded coconut to coat.
Place cookies 2 inches apart on ungreased baking sheets.
Bake until starting to brown but still soft to the touch, about 12-15 minutes.