In large bowl, beat butter with sugar until fluffy; beat in eggs, 1 at a time. Beat in vanilla. In a separate bowl, whisk together flour, baking powder and salt; add to butter mixture in 2 additions, stirring just until combined. Add pistachios and cranberries; mix well.

Divide dough in half. On lightly floured surface, shape each into 12-inch X 2 ½- inch rectangle. Place, 2 inches apart, on parchment paper–lined baking sheet; press to flatten slightly. Combine egg white with 1 tsp water; liberally brush over tops of biscotti.

Bake in 325ºF oven until light golden and just firm to the touch, about 30 minutes. Let cool on pan on rack for 10 minutes.

Transfer logs to cutting board. Using chef's knife, cut diagonally into 1/2-inch thick slices. Place cut side down, about 1/2 inch apart, on baking sheet. Bake in 300ºF oven until almost dry, about 35 minutes. Transfer to rack; let cool completely.

Dip 1 end of each biscotti in white chocolate, letting excess drip off. Place on waxed or parchment paper–lined baking sheet; refrigerate until chocolate is set, about 20 minutes.