Preheat oven to 350°F (180°C).

Lightly grease a large cookie sheet.

In a food processor, combine flour, sugar, lime zest, and baking powder until blended.

Add cold, cut-up butter and tart cherries to the food processor.

Pulse until cherries are coarsely chopped.

Spoon off 1 tablespoon of the beaten eggs and reserve for brushing.

Add remaining eggs and shelled pistachio nuts to the food processor.

Pulse until the dough is evenly moistened.

Turn the sticky dough out onto a well-floured work surface.

Divide the dough into quarters.

With your hands, roll each portion into a 9-inch log.

Place the logs crosswise 3 inches apart on the prepared baking sheet.

Press the logs to flatten them to about 2 inches wide.

Brush the flattened logs with the reserved beaten egg.

Bake for 25 minutes, or until golden brown.

Let the biscotti cool on the sheet on a wire rack for 10 minutes.

Loosen the biscotti with a spatula and remove them to a cutting board.

Let cool for 10 minutes longer.

Using a large, heavy knife, cut each log diagonally into 1/2-inch-thick slices.

Arrange the slices upright on a clean cookie sheet (no need to grease).

Bake for 14 to 15 minutes longer, until crisp.

Remove the biscotti to a wire rack to cool completely (they will get even more crisp as they cool).