Preheat the oven to 180°C (350°F). Generously grease an 18cm (7in) springform cake tin with butter and line the base with a circle of baking parchment.
Melt the butter in a small saucepan and set aside to cool slightly — it shouldn't be hot when it goes into the egg mixture in Step 4, or it can scramble the eggs.
Using an electric handheld mixer, beat the eggs and sugar together for 2–3 minutes, until the mixture has thickened, turned pale, and roughly doubled in volume.
Add the cooled melted butter and the yogurt (or kefir) to the egg mixture and beat for a further 30 seconds, until fully combined with no streaks of butter visible.
In a separate bowl, sift together the flour and baking powder.
Add the flour mixture and the pinch of salt to the egg mixture. Fold gently with a rubber spatula just until no dry flour remains — a few small lumps are fine, don't overmix.
Add the sliced apples and fold in just enough to distribute them evenly through the batter.
Pour the batter into the prepared tin and bake for 40–45 minutes, until a skewer inserted into the centre comes out clean.
Leave the cake in the tin for 5 minutes to firm up, then turn it out onto a rack, peel away the parchment, and leave to cool completely to room temperature before slicing.