Preheat the oven to 350°F.
Prepare (3) 9 inch round cake pans by spraying lightly with nonstick cooking spray and then lining with parchment paper. Cut a round for the bottom and then a long rectangle for the sides. Set aside.
Melt the white chocolate in a shallow, microwave safe bowl in the microwave at 50% power in 20 second intervals, stirring in between. Make sure not to burn the chocolate or over cook because it will seize. Set aside to cool slightly while you cream the butter and sugar together.
¾ cup white chocolate chips
In the bowl of a stand mixer, or a large bowl if using a hand mixer, beat the butter and sugar together until creamed, light and fluffy, about 3 to 5 minutes.
1 cup unsalted butter, 1 ½ cups granulated sugar
Add the melted white chocolate to the sugar mixture and mix until thoroughly combined.
Sift together the flour, baking powder, sea salt and baking soda into a large bowl.
3 ½ cups all purpose flour, 1 ½ teaspoons baking powder, 1 teaspoon fine sea salt, ½ teaspoon baking soda
In a medium bowl, whisk together the milk, yogurt, vanilla extract, peppermint extract and whipping cream.
1 ½ cups whole milk, 1 teaspoon vanilla extract, ⅓ cup plain Greek yogurt, ¼ to ½ teaspoon peppermint extract
Add the sifted dry ingredients, alternating with the wet ingredients, stirring just until combined. Be careful to not over mix.
In another medium bowl, use the whisk attachment to beat the egg whites until light and fluffy.
4 egg whites
Gently fold the egg whites into the batter. Be careful to not overmix.
Evenly divide the batter into three (use a scale if necessary) and pour into the prepared cake pans.
Bake cakes for 20 to 25 minutes or until the centers of the cakes spring back to the touch.
Let cakes sit in pan for 5 minutes before removing to a wire rack to cool completely.