Preheat your oven to 350°F (175°C) and grease a 9-inch cake pan, then set aside.
In a large mixing bowl, whisk together the eggs, sugar, and vanilla extract until the mixture is smooth and slightly frothy.
Pour in the melted butter and stir gently to combine, creating a rich, glossy mixture.
In a separate bowl, sift together the flour, salt, cinnamon, and nutmeg to evenly distribute the spices and dry ingredients.
Gradually fold the dry ingredients into the wet mixture, mixing gently until just combined and smooth.
Peel and grate the apples, then fold them into the batter, allowing their fragrant juice to meld into the mixture.
Pour the batter into your prepared cake pan and smooth the top with a spatula, ensuring an even layer.
Bake in the preheated oven for about 45 minutes, or until the top is golden brown and a toothpick inserted in the center comes out clean.
Remove the cake from the oven and let it cool in the pan for 10 minutes, then transfer to a wire rack to cool completely.
Once cooled, slice the cake to reveal the moist interior with hints of spiced apple, and enjoy its aromatic, tender crumb.
