Preheat oven to 325 degrees. Lightly coat a large baking sheet with nonstick cooking spray; dust with flour. In a small bowl, whisk together egg whites and honey until well blended; set aside. In large mixing bowl, combine flour, brown sugar, anise, baking powder, baking soda and salt. Make a well in center and add egg white mixture and apricots. Mix until dough is smooth and combined, about 1 minute. Transfer dough to lightly floured work surface; divide in half. Shape each portion into 12 x 2 inch log. Arrange logs on baking sheet, space about 6 inches apart. Bake until logs are golden brown, about 40 minutes. Reduce heat to 300 degrees. Transfer logs to work surface and let cool 3 minutes. Using sharp, serrated knife, slice each log diagonally into 1/2 inch slices. Arrange slices upright and slightly apart on baking sheet. Bake until crisp, about 15 minutes. Place cookies on wire rack and cool completely. Store in airtight container.