In a mixer with the paddle attachment, cream the butter. Add the powdered sugar and mix in. Add the vanilla extract and mix in. Add the dry ingredients and mix until blended.
Roll into 1 1/2-inch logs and roll in cornmeal to coat. Wrap in plastic wrap and chill at least one hour or overnight.
Preheat oven to 300 degrees F.
Slice shortbread dough thinly and bake on a silpat or parchment paper for 12 to 15 minutes. The shortbread will still be blonde, and they will crisp once cool.