Brown Butter Corn Flake Cake

Place a rack in middle of oven; preheat to 475°. Line a rimmed baking sheet with foil and spread out corn kernels on baking sheet. Roast, tossing halfway through, until slightly dried and beginning to brown around the edges, about 20 minutes. Let sit until cool enough to handle. Transfer to a food processor and pulse until finely chopped and only a few whole kernels remain.

Meanwhile, cook 1½ cups butter in a medium saucepan over medium heat, stirring often, until butter foams, then browns, 8–10 minutes. Transfer brown butter to a large bowl; let cool slightly.

Reduce oven temperature to 350°. Butter a 13x9" baking pan, then dust with cornmeal. Whisk flour, salt, baking powder, and remaining ½ cup cornmeal in a medium bowl.

Add brown sugar and granulated sugar to brown butter. Using an electric mixer on medium speed, beat just to incorporate the sugar, about 1 minute. Add eggs and vanilla and beat on high speed until light and creamy, about 4 minutes (this may seem like a long time, but it's necessary to get a thick cake). Reduce speed to low; add corn and beat to evenly distribute. Add dry ingredients and beat, occasionally scraping sides and bottom of bowl, just until combined. Scrape batter into prepared pan. Evenly scatter Corn Flakes over batter.

Bake cake until Corn Flakes are lightly toasted on edges and a tester inserted into the center comes out clean, 35–45 minutes. Let cool before serving.

Do Ahead: Cake can be made 1 day ahead. Wrap with plastic and store at room temperature.