Instructions

1. Heat the oven to 350°F. Pan-spray a quarter-sheet pan and line it with parchment paper, or just line it with a silicone baking mat.
2. Pulverize the popped popcorn, 1 cup at a time, in a blender until it is a fine powder, then sift it through a regular flour sifter. Continue this process until you have 50g (about 4 cups) of ground, sifted popcorn. Set aside the ground popcorn and put the remaining unground popcorn in a sealable plastic bag to use for the popcorn milk recipe.
3. Combine the butter and sugar in the bowl of a stand mixer fitted with the paddle attachment and cream together on medium-high for 2 to 3 minutes, until light and fluffy. Scrape down the sides of the bowl halfway through this process, and again at the end of it.
4. Add the eggs, one at a time, beating on medium-high for 1 minute after each addition. After you add the last egg, scrape down the sides of the bowl, then beat on high for 4 more minutes. Scrape down the sides of the bowl again.
5. Combine the buttermilk and oil and with the mixer on medium speed, stream them into the cake batter very slowly. It should take you approximately 3 minutes to add these liquids. Scrape down the sides of the bowl, increase the mixer speed to medium-high, and paddie for an additional 2 to 3 minutes, until the mixture is practically white, twice the size of your original fluffy butter-and-sugar mixture, and completely homogeneous. Don’t rush the process. You’re basically forcing too much liquid into an already fatty mixture that doesn’t want to make room for that liquid. There should be no streaks of fat or liquid. Stop the mixer and scrape down the sides of the bowl.
6. Whisk together the ground popcorn, cake flour, corn powder, baking powder, and salt.
7. With the mixer on very low speed, slowly add the dry ingredients and mix for 45 to 60 seconds, just until your batter comes together. Scrape down the sides of the bowl, then mix on low for an additional 45 seconds to make sure no lumps of cake flour get left behind.
8. Pour the cake batter into the sheet pan and, using a spatula, spread the batter in an even layer in the pan.
9. Bake for 30 to 35 minutes, rotating the pan front to back halfway through baking.  The cake will rise and puff, doubling in size, but will remain slightly buttery and dense. At 30 minutes, gently poke the edge of the cake with your finger: The cake should bounce back slightly and the center should no longer be jiggly. If it doesn’t pass these tests, leave the cake in the oven for an additional 3 to 5 minutes.