Preheat the oven to 350°F. Line a square baking pan with parchment paper and grease with nonstick cooking spray. Set it aside.
In a medium bowl, whisk together the flour, baking powder, and salt.
In a large mixing bowl, beat the eggs until foamy using an electric mixer at medium speed. Add sugar, melted butter, and vanilla until well combined. Fold in the apples. Pour the batter into the prepared cake pan.
Bake for 35 to 40 minutes or until a toothpick inserted into the center comes out clean. Let the cake cool in the pan for 20 minutes. Serve the cake warm or at room temperature. Dust with powdered sugar before serving.
For the Buttercream frosting
Using an electric mixer, whip the butter, powdered sugar, vanilla, heavy cream and salt for about 5 minutes or until smooth and fluffy.