Preheat the oven to 350°F [180°C]. Grease an 8-by-8-by-2-in [20-by-20-by-5-cm] square pan with nonstick cooking spray or softened butter, line with parchment paper, and grease again.
In a medium bowl, whisk together the flour, baking powder, baking soda, and salt.
In the bowl of a stand mixer fitted with the paddle attachment, beat the butter on medium-high speed until fluffy and light, 2 to 3 minutes, scraping down the bowl with a rubber spatula as needed.
Add the granulated sugar and vanilla and continue beating for another 3 to 5 minutes, until the mixture at least doubles in volume.
Decrease the speed to low and add the eggs and yolk, one at a time, scraping the bowl after each addition.
Add the dry ingredients in three additions, alternating with two additions of the buttermilk, scraping the bowl as needed with a rubber spatula. Stop the mixer and remove the bowl when there are still streaks of flour in the batter. Finish mixing by hand.
Slowly transfer the batter to the prepared pan (it will be very full) and bake for 35 to 45 minutes, mindfully rotating the cake at the halfway point. The cake is ready when a cake tester inserted in the center comes out with a moist crumb or two and the cake has just started to come away from the sides of the pan. If the edges get too brown before the cake is ready to be pulled from the oven, tent it with aluminum foil.
Let it cool for 10 minutes. Invert the cake onto a cooling rack, so it is right-side up, and let come to room temperature.
Vanilla Sauce Instructions
Whisk together the confectioners’ sugar and cornstarch in a small bowl.
Warm the cream over medium heat in a small saucepan. Once bubbles appear around the perimeter of the cream, add the sugar-cornstarch mixture and stir with a wooden spoon until thickened, 3 to 5 minutes.
Add the butter, vanilla, and salt and whisk to combine.
Transfer the cake to a serving plate and serve sliced and dribbled with the sauce and an optional dollop of whipped cream on the side.
The cake will keep, tightly wrapped in plastic wrap, on the counter for up to 3 days. The sauce can be refrigerated in an airtight container for up to 3 days. Reheat it in a microwave on high power for 30 to 60 seconds, or on the stovetop over medium heat until warm, before serving.