Preheat oven to 325 degrees. Line two baking sheets with parchment paper.
Sift together the dry ingredients (except the sugar) -- flour through espresso powder -- in a medium bowl. Set aside.
Beat butter at medium speed with an electric mixer until light and fluffy. Add in the powdered sugar, three to four tablespoons at a time beating well. Stir in dry ingredients by hand and beat just until blended.
Line 2 baking sheets with parchment paper. Divide dough into three equal balls. Take the first ball, place it between two sheets of plastic wrap, and pat or roll out into a 5 1/2 inch disk. Place on the far side of your baking sheet. Lightly score the disk and mark out 8 triangular wedges.
Repeat the patting, rolling and scoring for the other two disks, placing one on the other side of the first baking sheet and the third disk on the second baking sheet.
Bake rounds for 23 minutes or until shortbread feels firm to the touch. Remove from the oven.
Gently score each round again with a sharp knife following the lines you make on the dough. Slide parchment from baking sheets onto wire racks. Let shortbread cool completely on parchment. Cut shortbread into wedges along scored lines.
Melt unsweetened chocolate baking bars separately in small bowls according to package directions. You can do this in a microwave or on the stove using a double boiler. 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. (Alternately, if your house is cool you can let it set on it's own.)
Melt the white chocolate. Then partially dip other half of wide end of each wedge in white chocolate. Alternately, you can place in a plastic bag and stripe the cookies. Freeze briefly to set white chocolate or allow to air dry.