In a medium bowl, whisk together the flour and baking powder. Set aside.
In a large bowl or a stand mixer fitted with the paddle attachment, cream the butter, sugar, and salt on medium-high speed until light and fluffy, about 2-3 minutes.
Beat in the egg and vanilla extract until combined.
Gradually blend in the flour until well incorporated.
Divide the dough into two equal pieces. Shape each one into a ball, then press down to make a thick, flat disk (about 1 inch thick).
Wrap each disk in plastic wrap and refrigerate for at least 2 hours.
Preheat the oven to 350°F and line two large baking sheets with parchment paper.
Remove the dough and allow it to rest at room temperature for 20 minutes. Roll the dough on a lightly floured surface until ¼ thick.
Cut into desired shapes and place evenly spaced out on the prepared baking sheets.
Bake one sheet at a time for 9-11 minutes until the edges just start to turn golden brown.