Preheat the oven to 350 F. Grease and line an 8-inch or 9-inch cake tin (I prefer a loose-bottom one, resting on a tray).
In a medium bowl, whisk together the flour, baking powder, and salt. Set aside.
In a stand mixer fitted with the paddle attachment, beat the room temp butter and sugar for a minute, and then add the oil. Continue beating until well-combined and glossy, scraping down the sides of the bowl to ensure everything is incorporated.
Add the eggs and yolks one at a time, beating to fully incorporate between each. Add the vanilla.
In two additions, add the flour mixture, then milk, then the remaining flour, mixing on low in between the additions. Scrape the sides and bottom of the bowl and mix until JUST combined (don't overmix!).
Remove from the stand mixer and gently fold the corn kernels in with a rubber spatula, to avoid overmixing. Transfer the batter to your prepared pan.
Bake at 350 F for 30-40 minutes for a 9-inch cake and 35-45 for an 8-inch cake. The cake is done when a toothpick comes clean from the center (a few crumbs are fine).
Cool in the pan for 10-15 minutes, then turn out onto a cooling rack. Whisk up the glaze.
Once mostly cool, place on a serving plate and drizzle with the glaze. You can serve immediately, but I also really love this the next day.