Preheat the oven to 350 degrees Fahrenheit. Grease and flour a 9x13 baking pan, and set aside.
In a small bowl, sift in the flour, baking powder, baking soda, and salt. Set aside.
In a stand mixer, fitted with a paddle attachment, add the butter, and sugar and cream them together until they are light and fluffy, about 4 minutes.
Add in the eggs, one at a time, beating the mixture for 30 seconds after each egg is added.
Add the vanilla and beat it well into the mixture.
Gently fold the flour mixture into the egg and butter mixture, mixing until just incorporated. Use a rubber spatula to fold all the flour in until well blended.
Pour the batter into the prepared baking pan.
Bake the cake for 22 to 25 minutes.
Remove from the oven and use a bamboo skewer, or fork to poke the cake all over the top.