Preheat the oven to 180 degrees Celsius (350 Fahrenheit).
In a large bowl, crack the eggs, and add the sugar to them.
Use a hand mixer to beat them well until you have a creamy texture and a pale yellow colour.
Sift in the flour, add the baking powder, milk, oil and vanilla extract, and beat well to incorporate all the ingredients.
Peel the apples and slice them thinly on a grater.
Add them to a bowl and pour over the lemon juice.
Toss well to prevent the apples from browning too quickly.
Add the apples to the batter, and mix again.
Transfer the batter to a round baking tin (mine is 23 cm, or 9 inches in diameter) lined with non-stick paper.
Bake for 30-35 minutes or until the top is golden and a skewer inserted in the middle comes out clean.
Leave the cake to cool down completely before removing it from the pan.
Sprinkle it with icing sugar.