Sift flour, baking powder, and salt into a bowl.
Put butter and sugar in the bowl of an electric mixer fitter with the paddle attachment.
Mix on medium speed until pale and fluffy.
Add eggs and vanilla. Reduce speed to low and mix until combined.
Gradually add in the flour mixture and mix on low increasing speed as needed. Add a little at a time and mix just until combined.
Divide dough into 3-4 discs.
Wrap each in plastic wrap.
Refrigerate until firm, at least one hour or overnight.
Preheat oven to 325. °
Let disk of dough stand at room temperature just until soft enough to roll, about 10 minutes.
Cut out your shapes.
Remove the excess dough and place the mat with the cutouts in the freezer until the dough is very firm, about 15 minutes.
Bake for 7-11 minutes. Baking times will vary so keep a close eye on them. Remove from oven and let them cool on wire racks.