Preheat the oven to 300º.
Line a cookie sheet with parchment paper.
In a small bowl, combine the oil and sugar well, then stir in the vanilla and almond extracts and eggs. Set aside.
With a mixer on lowest speed, mix the flour, salt, and baking powder.
Add in the oil mixture, and mix on lowest speed to form a dough.
Add in the candied red and green cherries and pistachio nuts and beat for only 2 or 3 seconds to incorporate. You don't want to mix too long or the cherry colors will bleed into the dough.
Wet your hands and form the dough into 2 logs, (12x2 inches each) on the parchment paper.
Bake the logs at 300° for 35-40 minutes or just until the logs are a light golden color on top.
Remove the pan to a wire rack and let the pan cool for 10 minutes.
Meanwhile, reduce the oven to 275º.
Remove the logs to a cutting board. Using a sharp straight-edged knife, cut the logs on the diagonal into ¾ inch slices.
Lay the slices back onto the parchment paper flat side down, separating the biscotti an inch apart.
Bake for another 5 minutes. They will still be soft to the touch.
Immediately transfer the biscotti from the pan to a wire rack to cool. They will harden a bit more as they cool. Leave them plain, or decorate as you wish when they are cooled. See suggested decorations in the tips below.
Store the biscotti in a covered tin or pan on top of the counter.