Preheat your oven to 350°F. Line 2 large baking sheets with parchment paper, and set aside.
In a medium bowl, combine flour, baking powder, and salt. Whisk to incorporate and set aside.
In a large bowl, combine sugar, butter, and oil. Using an electric or stand mixer, or a wooden spoon, cream together until the sugar has fully dissolved and you have a relatively smooth mixture. Some graininess is normal and fine!
Whisk the eggs into the sugar mixture, one at a time, until incorporated. Add in your vanilla extract and mix to combine.
Pour your dry ingredients into the sugar/egg mix. Fold everything together until you get a thick sticky dough.
Divide the dough in half and transfer each half onto its own parchment lined baking sheet. With lightly floured hands or a spoon/spatula, pat each half of dough into a log that's about 3/4 of an inch thick and roughly 6 inches long.
Bake the logs in the center of your preheated 350°F oven for 20 to 25 minutes, or until lightly browned. Take the logs out of the oven (but leave the oven on). Set aside to cool for about 10 minutes on the baking sheet, or until cool enough to handle. The logs should still be quite warm to get the cleanest cuts!
Transfer one of the baked logs onto a cutting board. Use a serrated knife to cut the log into slices (on a slight angle) that are about 1/2 an inch to 3/4 of an inch thick. Arrange the slices cut side up on your baking sheet, leaving about 1/4 inch space between each one to allow for air to circulate. Repeat with the second log.
Transfer back into your preheated 350°F oven, and bake for another 10 to 12 minutes. Flip the biscotti about halfway through the bake so they dry evenly. The biscotti are ready once they're crisped up and lightly browned on top. The centers will still be soft, but they will firm up as they cool.
Take the biscotti out of the oven, and transfer onto a wire rack while they're still hot. Set aside to cool completely to room temperature before serving!