Preheat oven to 350 degrees. In an 8-inch ovenproof skillet, preferably cast iron, combine 1/4 cup sugar with 2 tablespoons water, stirring to make sure all of sugar is damp. Cook over high heat, stirring occasionally, until sugar turns a golden caramel brown, about 2 minutes. Remove pan from heat and whisk in 2 tablespoons butter.
Tightly layer apple rings over caramel, starting with outside of skillet and working toward the center, overlapping slices.
In a bowl of an electric mixer on medium speed, beat remaining 3/4 cup sugar, remaining 6 tablespoons butter and vanilla until light and fluffy, about 3 minutes. Add egg yolks, one at a time, beating well after each addition. In a medium bowl, whisk together flour, cornmeal, baking powder and salt. Reduce speed to low and, in three additions, add flour mixture to batter, alternating with milk and beginning and ending with flour mixture, scraping sides of bowl as necessary.
Transfer batter to another mixing bowl, and carefully clean and dry bowl of electric mixer. Using a whisk attachment, whip egg whites on medium-high speed until they reach soft peaks, about 4 minutes. In three additions, fold egg whites into batter.
Spread batter evenly over apples in skillet. Bake, rotating skillet halfway through, until cake is golden brown and firm to the touch, 45 to 50 minutes. Transfer skillet to a wire rack and cool just until cake is warm, about 30 minutes. Run knife around edge of cake and invert cake onto a serving plate. Serve warm or at room temperature.
Nutrition information per serving: