From Cook’s Illustrated magazine.
Topping: 4 tablespoons (1/2 stick) unsalted butter, cut into 4 pieces, plus extra for pan 4 Granny Smith apples or Golden Delicious (about 2 pounds), peeled and cored 2/3 cup packed light brown sugar (4 2/3 ounces) 2 teaspoons juice from 1 lemon Cake: 1 cup unbleached all-purpose flour (5 ounces) 1 tablespoon cornmeal (optional) 1 teaspoon baking powder 1/2 teaspoon table salt 3/4 cup granulated sugar (5 1/4 ounces) 1/4 cup packed light brown sugar (1 3/4 ounces) 2 large eggs 6 tablespoons (3/4 stick) unsalted butter, melted and cooled slightly 1/2 cup sour cream 1 teaspoon vanilla extract
FOR THE TOPPING: Butter bottom and sides of 9-inch round, 2-inch-deep nonstick cake pan; set aside. Adjust oven rack to lowest position and heat oven to 350 degrees.
Halve apples from pole to pole. Cut 2 apples into 1/4-inch-thick slices; set aside. Cut remaining 2 apples into 1/2-inch-thick slices. Heat butter in 12-inch skillet over medium-high heat. When foaming subsides, add 1/2-inch-thick apple slices and cook, stirring 2 or 3 times, until apples begin to caramelize, 4 to 6 minutes. (Do not fully cook apples.) Add 1/4-inch-thick apple slices, brown sugar, and lemon juice; continue cooking, stirring constantly, until sugar dissolves and apples are coated, about 1 minute longer. Transfer apple mixture to prepared pan and lightly press into even layer. Set aside while preparing cake.
FOR THE CAKE: Whisk flour, cornmeal (if using), baking powder, and salt together in medium bowl; set aside. Whisk granulated sugar, brown sugar, and eggs together in large bowl until thick and homogeneous, about 45 seconds. Slowly whisk in butter until combined. Add sour cream and vanilla; whisk until combined. Add flour mixture and whisk until just combined. Pour batter into pan and spread evenly over fruit. Bake until cake is golden brown and toothpick inserted into center comes out clean, 35 to 40 minutes.
Cool pan on wire rack 20 minutes. Run paring knife around sides of cake to loosen. Place wire rack over cake pan. Holding rack tightly, invert cake pan and wire rack together; lift off cake pan. Place wire rack over baking sheet or large plate to catch any drips. If any fruit sticks to pan bottom, remove and position it on top of cake. Let cake cool 20 minutes (or longer to cool it completely), then transfer to serving platter, cut into pieces, and serve.