Preheat your oven to 350°F (175°C). Line baking sheets with parchment paper or silicone baking mats.
In a large mixing bowl, cream together the softened butter and granulated sugar until light and fluffy, about 2-3 minutes.
Add the egg and vanilla extract to the butter-sugar mixture, and beat until well combined.
In a separate bowl, whisk together the all-purpose flour, baking powder, and salt.
Gradually add the dry ingredients to the wet ingredients, mixing until a smooth dough forms. Be careful not to overmix.
Shape the dough into small balls, about 1 tablespoon each. Alternatively, you can roll the dough into a log and slice it into rounds.
Place the shaped cookies onto the prepared baking sheets, spacing them about 2 inches apart to allow for spreading.
Transfer the baking sheets to the oven and bake for 10-12 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.
Once cooled, store the butter cookies in an airtight container at room temperature for up to one week.