Preheat oven to 180C/360F and adjust a baking rack onto the middle shelf. Grease and dust with flour (or line with parchment paper) a 9-inch cake pan and set it aside.
In a large bowl, place the eggs and the sugar. Beat the mixture with an electric whisker until light and pale, then gently whisk in the olive oil, followed by the vanilla, and mix until all the ingredients are combined.
3 large free-range eggs, 140 g sugar (or fine demerara sugar), 120 ml lightly-flavoured extra-virgin olive oil, 1 teaspoon vanilla extract
Slowly incorporate the flour into the batter, mixing until just combined. Sprinkle the baking powder and a pinch on salt over the batter and mix until just combined (do not overmix).
Fold into the batter 1-½ apples cut into tiny chunks, and lemon zest, and mix until just combined.
1 tablespoon baking powder, 600 g Honeycrisp apples, peeled and cored
Pour the apple cake batter into the prepared baking pan. Top the batter with the remaining 1-½ apples cut into thin slices, and bake in the oven for approximately 30-40 minutes. To check if the cake is ready, insert a toothpick in the middle, if it comes out clean, the cake is ready.
Remove from the oven, allow to cool and gently remove the apple cake from the pan.
Dust the cake all over with confectioner sugar and serve at room temperature.
1 tablespoon confectioner sugar