Whisk together the eggs. Add the sugar, and whisk until combined. Add the vanilla extract, vegetable oil, yogurt, and coffee, and whisk until combined. Gradually fold in the dry ingredients.
Divide the batter between the prepared cake pans, and bake for about 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.
Using a handheld or stand mixer, beat the butter until pale and creamy. Add half of the icing sugar, and beat until combined. Add the remaining icing sugar, and beat until smooth and combined. Add the coffee, and milk, and beat until light and fluffy. Add more milk if needed.
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, and spread on a layer of frosting. Top with the 2nd layer of cake 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, leaving some for piping swirls on top, if desired.
*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.
For a more stronger coffee flavour in the cake layers, add 6 teaspoons of coffee dissolved in 3 tablespoons of hot water.
After the cake layers have cooled completely, they can be wrapped in clingfilm and kept at room temperature or refrigerated/frozen overnight, ready to be frosted the next day. The frosting can also be stored in an airtight container and refrigerated overnight.
Frosted cake freezes well for up to 2 months.
The calories are an estimate only.