Preheat the oven to 350°F (175 °C). Prepare an 8-inch (20-cm) pan by greasing and flouring it, then lining it with a parchment round. Set aside for later.
In a bowl, whisk together the flour, baking powder, and salt. Set aside for later.
In the bowl of an electric mixer fitted with the paddle attachment, cream together the butter and sugar on medium for several minutes until it is very light and fluffy, scraping down the sides of the bowl and the beater as needed.
Beat in the eggs, one at a time, being sure to work in the first completely before adding the second.
Add the vanilla extract. Whip the mixture until it is light and fluffy.
Incorporate the dry ingredients on low, alternating with the wet. Don't overbeat the cake batter at this stage!
Transfer the cake batter to the prepared pan and smooth it with an offset spatula. Tap the pan on the counter a few times to get rid of any air bubbles.
Bake the cake til a cake tester inserted in the center comes out clean (about 35 minutes).
Cool for 15 minutes before flipping the cake out of the pan onto a wire rack to cool completely.
Notes
Calories calculated for one-twelfth of the cake (one slice)