Preheat oven to 325 degrees F (165 degrees C). Line a large baking sheet with parchment paper.

In a large bowl, combine sugar, melted butter, vanilla, baking powder, and salt.

Add eggs and egg whites, beating well until incorporated.

Fold in dried apricots and most of the chopped pistachios (reserving some for topping).

Gradually stir in flour and cornmeal until well blended. Use hands if necessary.

Let the dough rest for 5 minutes to firm up.

Divide the dough in half.

Shape each half into an 8x4-inch loaf on the prepared baking sheet, spacing them 4 inches apart.

Pat each loaf to an even thickness.

Bake for 24-28 minutes, or until firm and light brown. A toothpick inserted near the center should come out clean.

Remove from oven and cool completely.

Transfer to a cutting board and slice each loaf into 1/4-inch thick slices using a serrated knife.

Place slices, cut side down, on parchment-paper-lined baking sheets.

Return one baking sheet to the oven.

Bake slices for 12-14 minutes, or until toasted and light brown, turning once halfway through baking and watching carefully to avoid burning.

Slide the parchment paper with baked cookies onto a wire rack and let cool.

Repeat with the remaining slices.

In a microwave-safe bowl, melt chocolate and shortening in 30-second intervals, stirring until smooth.

Dip one half of each biscotti crosswise into the melted chocolate.

Allow excess chocolate to drip off and place on clean parchment paper.

Sprinkle with the remaining chopped pistachios.

Let stand until the chocolate is set.