Preheat your oven to 350F (175 C) and position a rack in the middle. Grease and flour a 9-inch cake pan or line it with parchment paper.
Beat the eggs and sugar in a large bowl until the mixture is light and pale. This can be done with a whisk or an electric mixer. Continue by gently whisking in the olive oil and vanilla extract until it's fully incorporated.
Gradually add the sifted flour to the egg mixture and mix until just combined.
Sprinkle the sea salt and baking powder over the batter, then gently fold them in until just mixed.
Add half of the apple slices and lemon zest to the batter and mix gently until the ingredients are evenly distributed.
Pour the batter into the prepared pan and smooth the top with a spatula. Arrange the remaining apple slices on top.
Bake for approximately 30-40 minutes or until a toothpick inserted into the center of the cake comes out clean.
Once it's fully baked, remove the cake from the oven and let it cool in the pan for a few minutes.
Carefully transfer it to a wire rack to cool completely.
Before serving, dust the top of the cake with confectioner sugar (optional).