Preheat the oven to 350 degrees F. Lightly coat an 18x13 inch half-sheet pan with baking spray (the kind with flour incorporated works best), top with parchment paper, and coat with additional baking spray.

In a medium-sized bowl, whisk together the flour, baking powder, baking soda, and kosher salt. Set aside. In a large liquid measuring cup, combine the buttermilk, vegetable oil and vanilla extract.

In a stand mixer fitted with the paddle attachment, combine the butter, granulated sugar, and brown sugar on low speed and then slowly turn the mixer up to high speed and cream for 3-4 minutes until light and fluffy. Scrape down the sides. Turn down the speed to medium and add the eggs and yolks, one at a time, allowing each to fully incorporate, over the course of 4-5 minutes. Scrape down the sides all the way to the bottom. Turn the mixer speed down to low and alternate between adding the dry and wet ingredients, starting and ending with the dry.

Scrape the batter into the prepared sheet pan, using a spatula (preferably an offset spatula) to even out the top of the cake. Make sure the batter is spread evenly into the 4 corners of the pan. Bake for 20-25 minutes, rotating the pan once halfway through, until the top is golden and springy, and a toothpick comes out clean from the center. Remove from the oven and allow to cool completely. The cake can be prepared 24 hours in advance (or longer, if frozen).

Gently run a pairing knife or offset spatula along the edges of the pan to detach any portion of the cake that might have attached itself. Next, place a clean dishtowel on top of the cake, and top that with another sheet pan or a large cutting board. Pick up the pan and gently flip it over so that the cake inverts onto the dish towel.

Peel away the parchment paper, and then gently flip the cake on a large serving platter, cutting board, or back into the same sheet pan (place the board or pan directly against the cake before inverting).

Frost the cake evenly and cut into squares. Serve.