Preheat oven to 350ºF and line a baking sheet with parchment paper.
Whisk the flour, baking powder, and salt together in a bowl. Set aside.
In a stand mixer (or using a bowl and a handheld electric mixer), cream together the butter, sugar, and vanilla bean until the mixture is light and fluffy and the vanilla bean is evenly dispersed. Beat in the eggs one at a time until well-incorporated, scraping down the bowl and beater as needed. Beat in the vanilla extract.
Add the dry ingredients to the wet and mix in on lowest speed, just until evenly incorporated.
Transfer dough to the prepared baking sheet and lay a second piece of parchment paper on top. Roll out to a 12" x 5 1/2" rectangle.
Bake in preheated oven for 30 minutes. Allow to cool for 5-10 minutes, just until no longer too hot to touch. Carefully slice into individual biscotti and turn onto one of the cut sides. Return to oven on second-lowest rack and bake another 15 minutes at 350ºF, and then flip biscotti and bake another 15 minutes on opposite side. Check the biscotti and remove any that are fully cooked (the edges pieces might be done). Otherwise, continue to bake another 5-10 minutes, until fairly firm on both sides; they will get crunchier as they cool.
Let biscotti cool on pan completely. Store in an airtight container at room temperature.