Preheat the oven to 170C/325F/Gas 3. Grease three 8-inch cake pans and line the bases with parchment paper. Set aside.
Whisk together the flour, cocoa powder, baking powder, baking soda, and salt. Set aside.
Whisk together the eggs and sugar until combined. Add the peppermint extract, butter, and yogurt, and whisk until combined. Gradually fold in the dry ingredients.
Divide the batter between the prepared cake pans, and bake for 30 - 35 minutes or until a toothpick inserted into the centre comes out clean. Allow to cool completely in the pans on a wire rack.
Once cooled, invert the cakes onto the wire rack and remove the parchment paper.
For the Frosting
In the heat-proof bowl of your stand mixer over a pan of simmering water, add the egg whites and sugar. Whisk constantly until the mixture is warm to the touch and all the sugar has dissolved (should not feel gritty between your fingers) - about 5 - 10 minutes.
Attach the bowl to the stand mixer fitted with the whisk attachment. Whisk on high speed for 10 - 15 minutes until the meringue reaches stiff peaks, and is completely cool.
With the mixer on medium-low speed, gradually add the butter, piece by piece, mixing well after each addition. If the mixture starts to look curdled, whip on high speed until it becomes smooth, then continue adding the butter.
Once all the butter has been added, whisk in the peppermint extract and food colouring. Whisk until silky and smooth.
To assemble, slice a thin layer off the tops of the cakes to create a flat surface. Place 1 cake layer on a cake stand or serving plate. Spread on a layer of frosting, sprinkle on a handful of chocolate chips, then top with the 2nd layer and repeat.
Top with the final layer, and cover the entire cake with a thin layer of frosting to lock in the crumbs. Refrigerate for about 30 minutes until the frosting is firm, then spread with the remaining frosting, reserving some for piping if desired. Decorate with chocolate chips!
Notes
*Make your own cake flour! Measure out 3 and 3/4 cups (468g) of plain/all-purpose flour, remove 7 tablespoons, and replace with 7 tablespoons of cornflour/cornstarch. Sift well.After the cake layers have cooled completely, they can be wrapped in clingfilm and refrigerated/frozen overnight, ready to be frosted the next day. The frosting can also be refrigerated overnight. You may need to re-whip it until silky and smooth. Frosted cake freezes well for up to 2 months.