Preheat the oven to 325°F (163°C). Grease and flour a 9×13-inch baking pan, tapping out excess flour.
In a medium bowl, whisk together the sifted all-purpose flour, baking powder, baking soda, and salt. Set aside.
In a large mixing bowl, beat the softened unsalted butter with an electric mixer on medium speed until creamy, about 1 minute.
Gradually add the granulated sugar to the butter, beating on medium-high speed until light and fluffy, about 3 to 5 minutes.
Add the eggs one at a time, beating well after each addition to fully incorporate.
Mix in the pure vanilla extract.
Reduce the mixer speed to low. Alternately add the dry flour mixture and the buttermilk to the butter mixture, beginning and ending with the flour mixture. Mix just until combined after each addition; do not overmix.
Pour the batter evenly into the prepared baking pan and smooth the top with a spatula.
Bake in the preheated oven for 40 to 45 minutes, or until a toothpick inserted into the center comes out clean.
Remove the cake from the oven and allow it to cool in the pan on a wire rack for 15 minutes.
Run a knife around the edges of the cake to loosen it from the pan, then invert onto a serving platter or cooling rack to cool completely before slicing and serving.