In a 9 to 10-inch skillet, melt 1 3/4 sticks butter over low heat. Add 3/4 cup sugar to the pan and stir around, then place apple slices, cut side down, in the pan. Don’t pack them too tightly, but try not to leave overly large gaps. Allow this to cook over low/medium-low heat while you make the cake batter.
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FOR THE CAKE:
In the bowl of an electric mixer, beat 1 stick of butter and 2/3 cup sugar until light and fluffy. Mix in vanilla and eggs. Add sour cream and mix well.
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In a bowl, mix flour, baking powder, salt, and cinnamon. Stir together then gradually add flour mixture into the creamed mixture until just combined. Gently stir in 1 chopped apple.
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Remove skillet from heat. Spoon batter over the top, then spread gently so batter is evenly distributed. Bake for 20 to 25 minutes, or until cake is golden brown and bubbly. Allow cake to sit in skillet for five minutes, then invert onto a serving plate. Don’t worry if some of the topping isn’t perfect—it’ll taste perfect!
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Serve warm with vanilla ice cream.
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NOTE: Use at least a 10 inch skillet due to the fact it might bubble over into your oven. You may want to put a pan under the skillet if it is smaller than 10 inches.