In a medium-sized mixing bowl, beat the eggs, sugar, baking powder, salt, vanilla, and espresso powder until creamy looking and thick like pancake batter.
Lower the mixer speed and add the flour, beating gently until it's totally incorporated.
Fold in the hazelnuts.
Transfer the dough to a parchment- or Silpat-lined baking sheet and shape it into a log about 14 inches long, 2 1/2 inches wide, and 3/4 inch thick.
Smooth the top of the log with a wet dough scraper.
Bake for 25 minutes.
Remove from the oven and let cool on the baking sheet for 5 to 25 minutes.
5 minutes before cutting, use a spray bottle of room temperature water to lightly but thoroughly spritz the log, making sure to cover the sides and the top. Softening the crust just this little bit will make slicing the biscotti easier.
Reduce the oven temperature to 325 F. Wait another five minutes and cut the biscotti into 3/4 inch slices. Slice in a straight up and down motion on the diagonal to produce biscotti slices long enough for dunking.
Set the biscotti upright back on your cookie sheet and bake for 25 minutes.
Place on a cooking rack to cool.
Mix powdered sugar and eggnog until smooth.
Transfer to a plastic sandwich bag and make a very tiny cut in the corner.
Squeeze the glaze out in whatever pattern you like onto the cooled biscotti.
Biscotti can be stored at room temperature for two weeks.