Cream softened butter and granulated sugar together in a large bowl until the mixture is light and fluffy.

Beat in the large egg and vanilla extract until well combined.

In a separate bowl, whisk together the all-purpose flour, baking powder, and salt, then gradually add the dry ingredients to the wet ingredients, mixing until just combined.

Divide the dough into two flattened discs, wrap each tightly in plastic, and chill in the refrigerator for at least 1 hour.

Preheat your oven to 375°F (190°C) and line baking sheets with parchment paper.

On a lightly floured surface, roll out one chilled dough disc to about ¼-inch thickness and cut into desired shapes using cookie cutters.

Place cookies on the prepared baking sheets and bake for 8-10 minutes, or until the edges are lightly golden.

Allow the cookies to cool on the baking sheets for a few minutes before transferring them to a wire rack to cool completely.