Preheat oven to 350°F (180°C). Line a pan with slightly oiled parchment paper. I recommend an 8-inch or 9-inch round pan for a thin cake with a custard soft texture or use a 9-inch x 5-inch loaf pan to serve slices but note that the texture will be denser and a bit gummy - but that's how my kids love it! Set the pan aside.
In a bowl, add egg yolk and yogurt. Whisk to bring ingredients together.
Sift the flour into the bowl and stir to combine and form a smooth thick cake batter. Set aside.
In another large mixing bowl, add the egg white and whisk with an electric beater until a stiff peak forms.
Gently fold the egg whites into the cake batter until no more egg white can be seen. The batter should be light and fluffy with no lumps.
Pour into the prepared pan.
Bake for 40-55 minutes at 350°F (180°C) or until a pick inserted in the middle of the cake comes out with just a few crumbs on it.
Cool the cake down on a wire rack. The cake will sink down in the middle, and that's normal.
Serve with dusted icing sugar on top or with jam on slices.
Store in the fridge up to 3 days in an airtight container or freeze for later and thaw at room temperature.