Preheat your oven to 350°F (175°C).

Line your baking sheets with parchment paper.

In a bowl, whisk together the flour, baking powder, and salt.

In a separate bowl, cream the softened butter and granulated sugar using an electric mixer.

Add the egg and vanilla extract to the butter mixture, mixing until well combined.

Gradually add the dry ingredient mixture to the wet ingredients, mixing until just combined.

Wrap the dough in plastic wrap and refrigerate for at least 1 hour.

On a floured surface, roll out the chilled dough to about 1/4 inch thick.

Use cookie cutters to cut out your desired shapes and place them on the prepared baking sheets.

Bake in the preheated oven for 8 to 10 minutes, or until the edges are lightly golden.

Let the cookies cool on the baking sheets for a few minutes before transferring them to a cooling rack.