Preheat the oven to 180C/350F/Gas 4, and grease a 13x9-inch pan. Set aside.
Whisk together the eggs. Add the sugar, and whisk until combined. Add the vanilla extract, oil, and yogurt, and whisk until combined. Gradually fold in the dry ingredients.
Pour the batter into the prepared pan, and spread out evenly. Bake for 20 - 25 minutes, or until a toothpick inserted into the centre comes out clean. Allow to cool completely in the pan on a wire rack before frosting.
Add half of the icing sugar, and beat until smooth and combined. Add the remaining icing sugar, cocoa powder, vanilla, and milk, and beat until smooth and spreadable. Add more milk if needed.
Spread the frosting evenly over the cooled cake, and garnish with your favourite toppings. Slice and serve!
*Make your own cake flour! Measure out 2 and 1/4 cups (280g) of plain/all-purpose flour, remove 4 tablespoons, and replace with 4 tablespoons of cornflour/cornstarch. Sift well.
Leftover cake can be stored, covered tightly, in the fridge for up to 3 days. Frosted or unfrosted cake can be frozen for up to 3 months. Thaw overnight in the fridge.
This cake can be made 1 day in advance, covered, and stored at room temperature. Cover the frosting, and store in the fridge until ready to use.
The calories are an estimate only.