
Heat the granulated sugar and the water in a medium saucepan over medium high heat. Stir at first to dissolve the sugar. Cook until bubbling, then continue to cook until the mixture *just* turns amber-colored. You need to pay close attention, because the sugar is at the verge of burning at this stage, and if you miss it the sugar will be unpleasantly burnt-tasting. You do NOT want it to be brown, just a nice golden-honey-color.
Remove the pan from the heat and add the brown sugar, cream, butter, and salt and stir to combine (the mixture may hiss and sputter a bit when you add them, this is normal). Place the pan over low heat and stir to dissolve any hardened clumps of sugar. Once everything is dissolved and the caramel is smooth, removed it from the heat.
The mixture should be drizzle-able, so if it's too thick after cooling a bit, add a tablespoon or two of water and stir until combined. Empty half of caramel mixture into a heat-safe bowl and set it aside (this caramel sauce will be served alongside the cake when it's done).
Grease and lightly flour an 8-inch cake pan and line the bottom with a parchment paper round. Preheat the oven to 350 degrees Fahrenheit.
Peel the apple and cut it into VERY thin slices across the equator, using a mandoline to slice it works best.
Take the remaining half of the caramel mixture, and pour half of *that* on the bottom of the cake pan, spreading it with a spatula so that it's evenly spread across the parchment paper on the bottom of the pan. Arrange the apple slices so that they're overlapping slightly on the bottom of the pan, starting at the edge and working in concentric circles towards the center. Pour the remaining half of the caramel sauce (which, just as a reminder, is really 1/4 of the total caramel sauce) over the apple slices. Set the pan aside.
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, lemon zest, and vanilla at medium speed until the mixture is pale and fluffy, about 5 minutes. Set aside. In a small bowl, whisk together the oil and the buttermilk (it's fine if they're separated).
Remove the bowl from the stand mixer and alternate between folding in the dry ingredients and the wet olive oil/buttermilk ingredients into the sugar mixture in four increments.
Pour the cake batter over the apples in the cake pan. Place the cake pan on a lipped baking sheet and bake in the oven until a toothpick inserted into the center of the cake comes out fairly clean, about 45 to 55 minutes.
Allow to cool for 10 minutes before inverting the cake onto the serving plate and allow to cool to room temperature. Transfer to a serving plate, slice, and serve alongside the remaining caramel sauce. If the sauce has thickened too much while it cooled, just heat it back up again and it will become more liquid in consistency.