Preheat oven to 175C (350F). Line a 20cm x 30cm (8×12 inch) baking tin with baking paper, leaving a 2cm overhang on all sides.
Place butter in a medium bowl and beat for 30 seconds with an electric hand/stand mixer.
Gradually add sugar on a low speed until the mixture is light and fluffy and has a mousse-like texture.
Whisk eggs in a small bowl with vanilla extract. With the mixer on low, slowly add the eggs and vanilla to the creamed butter and sugar, ensuring that it is all combined evenly.
Sift and whisk flour and baking powder together in a small bowl. Add half of the flour to the creamed mixture then fold it through to just combine. Add half the milk to the mixture, and fold to combine. Repeat this process with the remaining flour and milk, folding gently until the mixture is well combined (alternating the liquid and flour in this way prevents too much gluten from forming, ensuring a light and fluffy texture).
Spoon the mixture into prepared tin. It will seem like there is not enough mixture at first, but there is (don’t worry). Smooth out the mixture so that it is evenly distributed in the tin.
Bake for 20-25 minutes or until golden brown on the top, the edges of the cake pull away from the sides of the tin and/or a skewer comes out clean when inserted.
Let the sponge cool in the tin for 10 minutes before inverting onto a wire rack. Cool completely and trim the edges of the cake, then cut into squares (about 4-5cm).