Line a 9-inch round cake pan with grease and preheat the oven to 350°F (175°C).
In a large bowl, whisk together the eggs and sugar until light and fluffy.
Add the melted butter and vanilla extract, mixing until well combined.
Sift in the flour, baking powder, and salt, and fold gently into the wet ingredients.
Add the thinly sliced apples to the batter, ensuring they are evenly coated.
After the pan is ready, pour the batter into it and level it out.
Bake for 40 minutes or until a toothpick inserted into the center comes out clean.
Let the cake cool before dusting with powdered sugar and serving.