Preheat oven to 375 degrees F. Lightly grease a large cookie sheet; set aside. In a large mixing bowl beat butter with an electric mixer on medium speed for 30 seconds. Add syrup, baking powder, cinnamon, baking soda, and salt; beat until combined. Beat in eggs. Beat in as much of the all-purpose and whole wheat flours as you can with the mixer. Stir in any remaining flour and the apricots.
Divide dough in half. Shape each half into an 8-inch-long roll. Place rolls 3 inches apart on prepared cookie sheet; if necesary, flatten slightly until about 2 inches wide. Bake for 20 minutes or until firm and a wooden toothpick inserted near center of each log comes out clean. Cool on cookie sheet on a wire rack for 1 hour.
Preheat oven to 325 degrees F. Using a serrated knife, cut each log diagonally into 1/2-inch slices. Place slices, cut sides down, on an the cookie sheet. Bake for 8 minutes; turn slices. Bake for 8 minutes more or until dry and lightly browned. Transfer to a wire rack; let cool.
In a small saucepan heat white chocolate and shortening over very low heat until melted and smooth. Drizzle over biscotti. Place biscotti on waxed paper; let stand until chocolate is set.