Place half the shredded coconut in food processor with sugar, salt and baking powder. Process mixture until finely ground.
Add chilled butter pieces and process just until no lumps remain.
Add vanilla, the whole egg and egg yolk, reserving the egg white for the coating later. Process mixture just until it becomes smooth.
Add flour and pulse until a crumbly dough begins to form, being careful not to overmix.
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.