Heat the oven to 180 C / 355 F. Grease a 9-inch round cake pan and line the base with parchment paper.

In a large mixing bowl, whisk the eggs and granulated sugar together for about 2 minutes until the mixture is pale and slightly thickened.

Add the yogurt, oil, and vanilla extract to the bowl and whisk until smooth and fully combined.

Grate one apple over a clean cloth or paper towel, then squeeze firmly to remove as much juice as possible. Fold the grated apple into the wet mixture with a rubber spatula.

Add the flour, baking powder, and salt to the bowl. Fold gently until no dry streaks remain. Do not overmix.

Pour the batter into the prepared pan and smooth the top with the spatula.

Arrange the apple slices in an overlapping fan pattern over the batter surface. Press them in lightly so they sit flush.

Bake for 38 to 42 minutes, until the top is golden, the apple slices are caramelized at the edges, and a toothpick inserted into the center comes out clean. Tent loosely with foil after 25 minutes if the apple is browning too fast.

Cool in the pan for 10 minutes, then turn onto a wire rack. Dust with powdered sugar just before serving if using.