Combine first 5 ingredients in a medium bowl; set aside.
Beat butter at medium speed with an electric mixer until fluffy; gradually add powdered sugar, beating well. Stir in dry ingredients; beat just until blended.
Line 2 baking sheets with parchment paper. Divide dough into 3 equal portions. Place 2 portions on opposite ends of 1 baking sheet. Place remaining portion on second baking sheet.
Cover dough portions with plastic wrap; gently press or roll each portion of dough into a 5 1/2" circle. Lightly score each round with a sharp knife into 6 or 8 wedges.
Bake rounds at 325° for 23 minutes or until shortbread feels firm to the touch. Gently score each round again with a sharp knife. Slide parchment from baking sheets onto wire racks. Let shortbread cool completely on parchment. Cut shortbread into wedges along scored lines.
Melt chocolate baking bars separately in small bowls in the microwave according to package directions. Partially dip wide end of each shortbread wedge in unsweetened chocolate. Place on a wax paper-lined jelly-roll pan, and freeze briefly to set chocolate. Then partially dip other half of wide end of each wedge in white chocolate. Freeze briefly to set white chocolate.