Preheat the oven to 350°F (175°C). Line a cookie sheet with parchment paper or a silicone baking mat and set it aside.
In a medium-sized bowl, whisk together the flour, baking powder, and salt until well combined. Set this mixture aside.
In the bowl of a stand mixer fitted with the paddle attachment, add the softened butter and granulated sugar. Beat on medium speed for about 3 minutes, or until the mixture is pale and fluffy. This step helps create a light texture in your cookies.
Crack in the eggs one at a time, mixing well after each addition. Scrape down the sides of the bowl if needed to ensure everything is fully incorporated. Stir in the vanilla extract.
With the mixer on low speed, gradually add the dry ingredients to the butter mixture. Once everything is added, increase the speed slightly and beat just until the dough starts to come together and forms a soft ball. This should take about 2 minutes—don’t overmix.
Lightly flour your work surface and roll the dough to a thickness between 1/4 inch and 1/2 inch. Thicker cookies (closer to 1/2 inch) will be softer and more cake-like, while thinner ones will bake up slightly crispier. Avoid going thicker than 1/2 inch to ensure even baking.
Use your favorite cookie cutters to cut shapes from the dough. Carefully transfer each cookie to the prepared baking sheet, leaving a little space between each one.
Place the cookies in the oven and bake for 8 to 10 minutes, or until the edges are just starting to turn a light golden color. They may look slightly underdone in the center—that’s okay. They’ll finish setting as they cool.
Let the cookies rest on the baking sheet for 5 minutes before transferring them to a wire rack to cool completely. Enjoy them plain or decorate with your favorite frosting, glaze, or sprinkles.