Preheat the oven to 350°F (175°C). Grease a 9×13-inch baking pan or line it with parchment paper.
In a medium bowl, whisk together the all-purpose flour, baking powder, and salt. Set aside.
In a large bowl, using an electric mixer, beat the softened unsalted butter and granulated sugar together on medium speed until light and fluffy, about 3 to 4 minutes.
Add the eggs one at a time, beating well after each addition. Mix in the pure vanilla extract.
Gradually add the dry ingredients to the wet ingredients, mixing on low speed until just combined. Do not overmix.
Spread the cookie dough evenly into the prepared baking pan, smoothing the top with a spatula.
Bake in the preheated oven for 18 to 20 minutes, or until the edges are lightly golden and a toothpick inserted into the center comes out clean.
Remove from the oven and allow the bars to cool completely in the pan on a wire rack.
Once cooled, cut into 16 squares and serve.