Position a rack in the middle of the oven & preheat the oven to 350 degrees F. Line a large baking sheet with parchment paper.
In a large bowl, whisk together the flour, baking powder, salt, just 2 teaspoons of the ginger & 2 teaspoons of the cinnamon, as well as the cloves, the 3/4 cup of granulated sugar & all of the brown sugar.
In a medium bowl, whisk together the eggs, butter & vanilla extract, then pour this egg mixture into the flour mixture, stirring with a wooden spoon until dough comes together in a soft & slightly sticky mass.
Turn dough out onto a lightly floured work surface & knead several times until smooth.
Divide dough in half, then shape each piece into a log about 8 inches long & 2 inches wide before setting each log some 3 inches apart on the prepared baking sheet.
In a small bowl, stir together the remaining 1 teaspoon of ginger, 1 teaspoon of cinnamon & the 3 tablespoons of granulated sugar. Brush the logs with the egg white & sprinkle each log with 1/3 of the spiced sugar mixture.
Bake logs 25 to 30 minutes or until they are puffed & golden brown, then set the baking sheet on a wire rack to cool for 10 minutes.
Reduce oven temperature to 300 degrees F, then using a serrated knife, cut each log into 1/2-inch-slices (about 15 each).
Arrange the biscotti, flat-side down, on the baking sheet & sprinkle with another 1/3 of the sugar mixture, then bake for 6 minutes or until biscotti are light golden brown.
Turn the biscotti over, sprinkle with the remaining sugar mixture & bake another 6 minutes.
Cool biscotti on the baking sheet set on a wire rack for 5 minutes before removing them to the rack to cool completely.
Store in an airtight container or in a zip-lock bag for up to 4 days.