Grease an 8-inch cake pan and line the bottom with a parchment paper round. Preheat the oven to 350 degrees Fahrenheit.
Melt the butter in a medium skillet over medium heat. Add the corn syrup, 1/4 cup of the sugar, and cream and cook until the sugar dissolves, about 4 minutes, stirring every minute. Add the apples to the pan, cut side facing up, and allow to cook until they begin to release a bit of juice, about 4 minutes, without moving them. Flip them over and cook for another 4 minutes, then remove them and place the apples in the cake pan cut side facing down on the parchment paper. Pour the caramel from the skillet over the apples in the pan and place the pan in the refrigerator.
In a medium bowl, mix together the flour, almond meal, baking powder, cinnamon, salt, and baking soda until combined. Set aside.
In the bowl of a stand mixer fitted with the paddle attachment, beat the eggs, sugar, vanilla, and orange zest at medium speed until the mixture is pale and fluffy, about 5 minutes.
Remove the bowl from the stand mixer and fold in the dry ingredients in two increments. Fold in the olive oil 1/4 cup at a time.
Pour the cake batter over the apples in the cake pan. Place the cake pan on a baking sheet and bake in the oven until a toothpick inserted into the center of the cake comes out clean, about 50 to 60 minutes. Allow to cool for 10 minutes before inverting the cake onto a wire cooling rack to cool to room temperature. Transfer to a serving plate, slice, and enjoy.
I recommend using California Olive Ranch's 'everyday' blend for the olive oil in this recipe