1. Preheat oven to 350°F. Toast pistachios on ungreased baking sheet 4 to 6 minutes, or until pale brown and fragrant. Cool, and finely chop. Reduce oven temperature to 325°F.
2. Stir together flours, sugar, baking powder, and salt in large bowl. Stir in pistachios and apricots.
3. Whisk together eggs, oil, and almond extract in small bowl until smooth. Stir just enough of liquid into flour mixture until dry, shaggy dough forms. Reserve remaining liquid.
4. Divide dough in 2 pieces. Wet hands with water to prevent sticking, and roll each piece of dough into 12-inch log, flattening tops of logs so they’re each about 1 1/2 inches high. Line large baking sheet with parchment paper, and place logs at least 5 inches apart on sheet. Brush tops with remaining liquid mixture.
5. Bake logs 25 to 30 minutes, or until edges are browned and firm, and centers have puffed and developed a skin, but are still slightly soft. Cool 30 minutes, then slice crosswise on the bias into 1/2-inch-wide slices using serrated knife.
6. Reduce oven temperature to 300°F. Return sliced biscotti to baking sheet, bottom-side down and spaced at least 1/4 inch apart, and bake 20 to 30 minutes more, or until golden, crisp, and dry.