In a large mixing bowl beat butter with an electric mixer on medium to high speed for 30 seconds. Add powdered sugar; beat until combined. Beat in hard-cooked and raw egg yolks and vanilla. Beat in as much of the flour as you can with the mixer. Using a wooden spoon, stir in any remaining flour.
Cover and chill cough about 1 hour or until firm enough to handle. (Chilling it longer may make it too firm to roll.)
On a lightly floured surface, using about 1 tablespoon dough for each cookie, roll dough into 6-inch-long ropes. On an ungreased cookie sheet shape each rope into a ring, crossing it over itself about 1 inch from ends. Brush with egg white and sprinkle with pearl or coarse sugar.
Bake in a 325 degrees F oven for 18 to 20 minutes or until edges are lightly browned. Cool on cookie sheet for 1 minute. Transfer cookies to a wire rack; cool. Makes about 36 cookies.