Prepare the apples: Wash, core, and slice apples into thin wedges. Toss lightly with a teaspoon of sugar.
Beat eggs and sugar: In a large bowl, whisk eggs and granulated sugar until pale and fluffy (about 5 minutes).
Add flour and vanilla: Fold in flour, salt, and baking powder gently. Stir in vanilla extract.
Combine apples and batter: Fold apple slices into the batter. Leave a few slices on top for decoration.
Bake the cake: Pour the mixture into a greased 9-inch (23 cm) round pan. Bake at 350°F (175°C) for 35–40 minutes. Check with a toothpick; it should come out clean.
Cool and serve: Let the cake cool slightly before slicing. Dust with powdered sugar if desired.