In a mixing bowl, beat butter with an electric mixer on medium to high speed for 30 seconds. Add powdered sugar, almond extract, and salt. Beat until combined, scraping side of bowl occasionally. Beat in egg yolk until combined. Beat in as much of the flour as you can with the mixer. Using a wooden spoon, stir in any remaining flour and the 1 cup toasted coconut.
Divide dough in half. Shape each half into an 8-inch roll. Brush rolls with egg white, then roll in the 1 cup shredded coconut to coat. Wrap each roll in plastic wrap or waxed paper. Chill for 4 to 24 hours or until dough is firm enough to slice.
Preheat oven to 375 degrees F. Cut rolls into 1/4-inch slices. Place slices 1 inch apart on an ungreased cookie sheet. Bake for 10 to 12 minutes or until edges are lightly browned. Cool on cookie sheet for 1 minute. Transfer cookies to a wire rack and let cool.