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For the Caramel and Apples:
4 tablespoons unsalted butter, plus more for the pan
3 cups brown sugar
1-cup heavy cream
4 large apples
For the Batter:
3 cups white unbleached flour
2 teaspoons baking powder
1/2 tsp baking soda
1 tsp salt
1/2 tsp ground cinnamon
1/2 cup sour cream
1/3 cup fresh orange juice
1 Tbsp vanilla extract
1 Tbsp almond extract
1 stick unsalted butter, softened
1 1/2 cups brown sugar
3 eggs (Replacer (in this case): 1 mashed banana, 2 Tbsp cornstarch, ¼ cup warm water)
Butter a 9-by-3-inch round cake pan. Make the caramel: Cook the sugar, butter and cream in a large skillet over medium-high heat, stirring occasionally, until the sugar is dissolved and the mixture is medium amber, 5 minutes.
Remove the skillet from the heat and let sit 1 minute. Pour 1 1/2 cups caramel into a glass measuring cup and set aside. Pour the remaining caramel into the prepared pan and set aside until set, about 30 minutes.
Cut 3 apples into quarters and cut out the cores with a paring knife. Arrange the pieces skin-side down in the pan (overlapping them slightly) to form a ring about 1/2 inches from the edge. Save any pieces that do not fit for later. Chop the last apple in small cubes and set aside.
Halve the remaining whole apple crosswise and slice them into wedges.
Arrange the apple in the bottom of the pan, layering them side by side.
Preheat the oven to 350 degrees F. Make the batter: Whisk the flour, baking powder, baking soda, salt, cornstarch, cinnamon and nutmeg in a medium bowl. In a small bowl, whisk the sour cream, orange juice, almond and vanilla extract.
Using a stand mixer with the paddle attachment, beat the butter and sugar on medium-high speed until light and fluffy, about 5 minutes.
Add the banana and lukewarm water and beat until the mixture is pale and creamy, about 5 more minutes. Scrape down the bowl and beater with a rubber spatula.
With the mixer on low speed, add half of the sour cream mixture, then half of the flour mixture. Repeat. Turn off the mixer and scrape down the bowl with a rubber spatula; finish combining the batter by hand, mixing in the last cubed apple.
Spread the batter over the apples in the pan. Bake on the middle oven rack until the cake is brown on top and springs back when pressed, 1 hour to 1 hour 20 minutes (don’t worry if the top is dark).
Soften the reserved 1 1/2 cups caramel over low heat, about 2 minutes. As soon as the cake is out, poke with the end of a spoon about 50 thin holes into the cake and loosen the side of the cake from the pan. Pour the caramel over the cake and on the sides. Cool in the pan on a rack.
Adapted recipe from The Food Network source, originally a Paula Dean recipe.