Step 1: Preheat the oven to 350F, adjust the rack to the lowest position. Butter a 9" round, 2+" deep non-stick cake pan-set aside.
Step 2: Make the topping-
Step 3: Halve the apples from pole to pole. Cut 2 apples into 1/4" slices and set aside.
Step 4: Cut remaining 2 apples into 1/2" slices.
Step 5: Heat the 4 Tb of butter in a 12" skillet over medium-high heat-when foaming subsides, add the 1/2" apples slices and cook, stirring 2 or 3x, until the apples begin to caramelize, 4-6 minutes ( do not fully cook apples).
Step 6: Add the 1/4" apple slices, brown sugar and lemon juice-continue cooking, stirring constantly, until the sugar is dissolved and the apples are coated, about 1 minute.
Step 7: Transfer the apple mixture to the prepared pan and lightly press into an even layer.
Step 8: Make the cake-
Step 9: Whisk flour, cornmeal ( if using), baking powder and salt together in a medium bowl-set aside.
Step 10: Whisk white sugar, brown sugar and eggs together in a large bowl until thick and homogeneous. Slowly whisk in butter until it combines. Add sour cream and vanilla-whisk until combined. Add flour mixture and whisk until just combined.
Step 11: Pour the batter into the pan and spread evenly over the fruit.
Step 12: Bake, on the lowest oven shelf, until the cake is golden brown and a toothpick comes out clean-35-40 minutes.
Step 13: Cool pan on wire rack for 20 minutes then run a knife around the edge to loosen-place the wire rack over the cake pan-holding the rack tightly , invert cake pan and wire rack together to lift the cake off pan-place wire rack over a baking sheet to catch drips. Let the cake cool 20 minutes or more then transfer to a serving platter.
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