Preheat oven to 350°F (175°C) and line an 8-inch cake pan.
Whisk eggs and sugar until fluffy.
Add melted butter, salt, vanilla, and yogurt; mix well.
Fold in flour and baking powder gently.
Add apple slices, pour into pan, and bake for 35–40 minutes.
Cool and dust with powdered sugar before serving.
