Heat oven to 325º. In a small bowl, whisk together flour, baking powder, baking soda, and salt. In the bowl of a standing mixer, beat butter with sugar until light and fluffy. Beat in eggs one at a time. Add vanilla. Lower speed and beat in dry ingredients. Stir in pistachios and cranberries by hand.
Line a baking sheet with parchment paper or Silpat. Form dough into a log, 14 inches long by 4 inches wide by 1-½ inches high.
Bake until golden, about 30 minutes. Transfer baking sheet to a rack; let cool about 5 minutes. Using a serrated knife, slice log on the diagonal into ½-inch-thick pieces.
Arrange slices on a lined baking sheet and bake about 8 minutes per side. Transfer biscotti to a rack and cool completely. Drizzle with melted white chocolate. Refrigerate until set, about 10 minutes.