Preheat your oven to 350°F (175°C). Line baking sheets with parchment paper or silicone baking mats and set aside.
In a medium mixing bowl, whisk together the all-purpose flour, baking soda, and baking powder. Set aside.
In a large mixing bowl or the bowl of a stand mixer, cream together the softened unsalted 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.
Gradually add the dry ingredients to the wet ingredients, mixing until a smooth dough forms. Be careful not to overmix.
If desired, chill the cookie dough in the refrigerator for 30 minutes to 1 hour. Chilling the dough helps prevent the cookies from spreading too much during baking.
Once the dough is chilled (if applicable), roll it out on a lightly floured surface to about 1/4-inch thickness.
Use cookie cutters to cut out shapes from the rolled-out dough. If desired, you can roll the cut-out shapes in additional granulated sugar before placing them on the prepared baking sheets.
Place the cut-out cookies on the prepared baking sheets, spacing them about 2 inches apart to allow for spreading during baking.
Bake the cookies in the preheated oven for 8-10 minutes, or until the edges are lightly golden brown.
Remove the cookies from the oven and let them cool on the baking sheets for a few minutes before transferring them to wire racks to cool completely.
Once the cookies are completely cooled, you can decorate them with royal icing or frosting if desired.
Store the sugar cookies in an airtight container at room temperature for up to one week.