Heat oven to 350 degrees F. In bowl, combine flour, baking powder, and salt. In large bowl, with mixer on high, beat butter and sugar until light and fluffy, about 3 minutes. Add eggs, orange peel, and vanilla; beat 2 minutes more. Reduce mixer speed to low, and beat in flour mixture. Stir in apricots and pistachios.

Divide dough into 4 equal parts. Shape each part into a 12 inch log (about 1-1/2 inches thick). Place logs 3 inches apart on ungreased baking sheet. Bake 25 minutes. Let cool 10 minutes. Cut each log into 16 diagonal slices. Return slices to baking sheet, and bake 20 minutes more. Let cool completely. Dunk ends of biscotti into melted white chocolate, and place on sheets of wax paper. Let dry completely.