Preheat oven to 350 degrees F. Grease a 9-inch round cake pan. Trace the bottom of the cake pan on a piece of parchment paper and cut it to match. Line bottom of cake pan with the parchment.

In a medium bowl, whisk together the flour, baking powder, baking soda, and salt. Set aside.

In the bowl of a stand mixer fitted with the paddle attachment, or a large bowl if using a hand mixer, rub the sugar and lemon zest together with your fingertips until fragrant. Cream together the butter and lemon sugar on medium-high speed until pale and fluffy, 2-3 minutes.

Add the eggs one at a time, beating on medium speed until fully incorporated after each addition. Add the vanilla extract and beat briefly to combine.

Add a third of the flour mixture and beat on low speed until combined, then add half the buttermilk and beat on low speed again. Repeat with remaining third of flour mixture, the rest of the buttermilk, and end with the last third of the flour mixture. Beat on low speed until the batter is smooth, but do not overmix.

Scrape batter into the prepared pan and smooth it out with a spatula. Bake for 30-32 minutes, until lightly browned and a toothpick inserted in the center comes out clean. Let cake cool in pan on a rack for 10-15 minutes, then invert the pan onto the rack to release the cake, remove the parchment from the bottom, and flip back right side up onto a cake plate. Let cake cool before adding frosting.