Preheat oven to 350 degrees F (175 degrees C). Line a large baking sheet with parchment paper.
In a bowl, whisk together the flour, baking powder, salt, cinnamon, and cloves until well mixed. With an electric mixer on medium speed, beat the butter and sugar together in a separate large bowl until light and fluffy; beat in the eggs, one at a time.
Mix in the vanilla extract. Stir in the flour mixture just until incorporated, and mix in the cinnamon chips and pistachio nuts.
Divide the dough in half. With floured hands, shape each half into a log about 9 inches long, and place on the prepared baking sheet.
Brush the logs with beaten egg white.
Bake in the preheated oven until the logs are golden brown, 30 to 35 minutes.
Remove from oven and let cool until easy to handle. Reduce oven heat to 325 degrees F (165 degrees C).
Remove parchment paper from baking sheet.
Using a serrated knife with a light sawing motion, cut the logs apart into 1/2-inch thick biscotti.
Place the biscotti onto the baking sheet, and return to oven.
Bake in the oven until the biscotti are lightly toasted, about 10 minutes; remove from oven, turn the biscotti over, and toast the other sides for an additional 10 minutes. Allow to cool on wire racks.
