Preheat the oven to 180C/350F/Gas 4. Grease a 13x9-inch pan, and set aside.
Whisk together the flour, baking powder, baking soda, and salt. Set aside.
Whisk together the eggs. Add the sugar, and whisk until combined. Add the vanilla extract and vegetable oil, and whisk until combined. Gradually mix in the dry ingredients, alternating with the buttermilk.
Pour the batter into the prepared pan, and spread out evenly. Bake for 30 - 35 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.
For the Frosting
Using a handheld or stand mixer, beat together the butter and icing sugar until light and fluffy.
Beat in the milk and vanilla extract until smooth, and spreadable. Spread the frosting over the top of the cooled cake, then slice and serve.
Notes
*Don't have cake flour? Measure out 3 cups (375g) of plain/all-purpose flour, remove 6 tablespoons, and replace with 6 tablespoons of cornflour/cornstarch. Sift well.**To make your own buttermilk, simply measure out 1 cup (240ml) of milk, and stir in 1 tablespoon of lemon juice or white vinegar. Let stand for 5 - 10 minutes until the mixture starts to curdle, then it's ready to use!Leftovers can be stored, covered, in the fridge for up to 2 - 3 days.After the cake has cooled completely, it can be wrapped in clingfilm and refrigerated/frozen overnight, ready to be frosted the next day. The frosting can also be refrigerated overnight.Frosted or unfrosted cake freezes well for up to 2 months. Thaw overnight in the fridge.