Sift all of the dry ingredients and place in a 12-qt mixing bowl with the vanilla pod seeds.
Place the butter on top of the dry ingredients and insert the paddle attachment.
Turn the mixer on to low speed and mix until just combined. It should be a homogenous mass. It is a good idea to scrape the sides of the bowl and mix for a few more seconds to ensure an even mixture of ingredients. Be careful not to overmix the dough.
Place the shortbread dough onto a parchment-lined sheet pan and shape into a square with your hands. Cover completely with plastic wrap and refrigerate for at least 2 hours.
Preheat a convection oven to 160°C / 325°F.
Roll out the dough to 3 mm / .11 in thick. Score the dough with a fork and freeze for 30 minutes.
Bake the shortbread as a full sheet until golden brown around the borders, 6 to 8 minutes. Once it is baked, cut the dough into 5-cm / 2-in squares while it is still warm to get the cleanest cut.
Once the squares are cut, let the cookies cool. Transfer to an airtight container. Reserve in a cool, dry place for up to 48 hours.