Preheat the oven the 180°/350°. Grease and line a 9"x13" (23cm x 33cm) rectangular cake tin.
Whisk together the flour, baking powder and salt. Set aside. Melt the butter and allow it to cool while moving on to the next step.
250 grams plain flour, 4 teaspoons baking powder, ½ teaspoon table salt, 125 grams butter
In a large mixing bowl beat the eggs and sugar until light and fluffy and has doubled in volume. About 3-5 minutes using an electric hand mixer/stand mixer.
3 eggs, 300 grams white granulated sugar
Add in the vanilla and mix through. Then pour the butter slowly down the side of the bowl with the mixer running. Mix until well combined. Similarly, add in the milk and mix through.
125 grams butter, 4 teaspoons vanilla extract, 240 grams milk
Add in half the flour mixture and mix through on a low speed. Then add in the other half and mix until combined.
Pour the batter into the prepared baking tin. Smooth to the edges. Bake for 25 to 30 minutes or until a cake tester comes out clean from the centre of the cake. Cool in the tin for 10 minutes before turning out onto a cooling rack to completely cool.
To make the icing/frosting, beat the butter until the butter has lightened in colour. Add in the vanilla and salt, and beat together. (If using the stand mixer, use the whisk attachment).
230 grams butter, 1 tablespoon vanilla extract, ½ teaspoons table salt
Add in the icing sugar one third at a time, and mix thoroughly. Add in 4 to 8 tablespoons of milk (start with 4 and work your way up.) and mix until you have a soft spreading consistency. Then beat the frosting for 3 to 5 minutes until soft, fluffy and ready for spreading.
500 grams icing sugar, 1-4 tablespoons milk
Plop the frosting/icing over the top of the completely cooled cake, smooth until mostly even using an offset spatula or the back of a dessert spoon. Then create swirly patterns on the top if desired.