Preheat the oven to 350F and spray a 13 x 9 inch baking tin with cooking spray and line with parchment.
Using a stand mixer with the whisk attachment, beat both the egg whites and eggs until frothy. Slowly add in the sugar and whisk until white and creamy. Add the oil and two teaspoons of the peppermint extract and whisk until incorporated.
In a medium bowl combine the flour, baking powder and salt and gradually add this to the egg mixture alternating with one and a half cups of milk beginning and ending with the flour mixture. Beat until just combined after each addition – do not overmix
Stir in the melted white chocolate.
Spread into the prepared baking tin and bake in the oven for around 40 minutes until a toothpick inserted in the center comes out clean.
Allow to cool for ten minutes then using the handle of a wooden spoon, poke one inch holes into the warm cake every half an inch.
In a large bowl whisk together the instant pudding mixture with three and a half cups of milk and one teaspoon of peppermint extract until thickened and smooth.
Slowly pour over the cake. Cover and place in the fridge for a minimum of four hours.
To serve, cover with the thawed whipped topping and crushed peppermint candies