Preheat your oven to 350°F (175°C). Grease or line a 9x13 inch baking pan with parchment paper for easy removal.
In a medium bowl, whisk together the all-purpose flour, baking powder, and salt. Set this mixture aside.
In a large mixing bowl, use an electric mixer to cream together the softened butter and granulated sugar until light and fluffy, about 2-3 minutes.
Add the eggs, one at a time, mixing well after each addition. Then, mix in the vanilla extract until everything is well combined.
Gradually add the dry ingredient mixture to the wet ingredients. Mix just until combined. Be careful not to overmix, as this can affect the texture of your bars.
Spread the dough evenly into the prepared baking pan. Bake in the preheated oven for 20-25 minutes, or until the edges are lightly golden and a toothpick inserted in the center comes out clean.
Once baked, remove the pan from the oven and let the bars cool in the pan for about 10 minutes. Then, transfer them to a wire rack to cool completely.
While the bars are cooling, prepare the frosting. In a mixing bowl, beat together the softened butter and powdered sugar.