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1
Butter a 9-by-3-inch round cake pan.
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2
Make the caramel: Cook the sugar and corn syrup in a large skillet over medium-high heat, stirring occasionally, until the sugar is dissolved and the mixture is dark amber, 7 to 10 minutes.
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3
Reduce the heat to medium.
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4
Carefully add the cream and 4 tablespoons butter (it will splatter) and cook, stirring, until combined, about 3 minutes.
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5
Remove the skillet from the heat and let sit 1 minute.
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6
Pour 1 1/2 cups caramel into a glass measuring cup and set aside.
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7
Pour the remaining caramel into the prepared pan and set aside until set, about 30 minutes.
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8
Cut 3 apples into quarters and cut out the cores with a paring knife.
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9
Arrange the pieces skin-side down in the pan (overlapping them slightly) to form a ring about 1/2 inch from the edge.
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10
Save any pieces that do not fit for later.
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11
Halve the remaining whole apple crosswise.
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12
Scoop out the seeds with a melon baller or measuring spoon, leaving the stem on the top half.
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13
Chop the bottom and any of the leftover quartered apples into pieces; set aside.
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14
Arrange the apple top, stem-side down, in the center of the pan.
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15
If the quartered apples shift, just push them back into place.
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16
Preheat the oven to 350 degrees F. Make the batter: Whisk the flour, baking powder, baking soda, salt and cinnamon in a medium bowl.
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17
In a small bowl, whisk the sour cream, orange juice and vanilla.
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18
Using a stand mixer with the paddle attachment, beat the butter and sugar on medium-high speed until light and fluffy, about 5 minutes.
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19
Crack the eggs into a small bowl.
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20
Slip them into the mixer bowl, one at a time, and beat until the mixture is pale and creamy, about 5 more minutes.
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21
Scrape down the bowl and beater with a rubber spatula.
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22
With the mixer on low speed, add half of the sour cream mixture, then half of the flour mixture.
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23
Repeat.
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24
Turn off the mixer and scrape down the bowl with a rubber spatula; finish combining the batter by hand.
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25
Spread the batter over the apples in the pan.
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26
Top with the chopped apple.
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27
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).
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28
Cool in the pan on a rack.
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29
Bring 1 inch of water to a simmer in a skillet wide enough to hold the cake pan.
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30
Carefully run a sharp knife around the inside of the pan several times, then rest the pan in the water to soften the caramel, about 8 minutes.
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31
Remove the pan from the water and dry.
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32
Invert a plate on top of the cake, then flip over the cake and plate.
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33
Using pot holders or a towel, wriggle the pan off.
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34
Soften the reserved 1 1/2 cups caramel in the microwave, about 2 minutes.
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35
Drizzle the cake with some of the caramel.
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36
Slice and serve with the rest.
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37
Photographs by Kana Okada