Sift flour, baking powder, and salt into a bowl.
Add butter and sugar to the bowl of an electric mixer fitted with the paddle attachment. Mix on medium speed until pale and fluffy.
Add the eggs and vanilla and mix.
Gradually add the flour mixture one cup at a time and mix until it is all combined.
Divide dough into 3 discs and wrap with plastic wrap. Refrigerate until firm, at least one hour or overnight.
Preheat oven to 375°
Let disk of dough stand at room temperature just until soft enough to roll, about 10 minutes.
Bake for 6-9 minutes.