Preheat the oven to 160°C fan (180°C conventional / 350°F) and line an 8-inch square baking tin with parchment paper.
Cream together the butter and sugar until pale and fluffy - about 2-3 minutes with a stand mixer or an electric hand mixer.
Add the eggs one at a time, beating well after each addition, then mix in the vanilla extract.
Sift in the flour and gently fold it into the mixture. Add the milk a tablespoon at a time until the batter is smooth and drops easily from a spoon.
Pour the batter into your prepared tin, level the top, and bake for 45-50 minutes, or until golden brown and springy to the touch.
Cool your cake in the tin for 10 minutes, then transfer to a wire rack to cool fully before icing.
Make the icing by combining icing sugar with a little milk or water until smooth and spreadable (you want a thick, pourable consistency).
Spread the icing over the cooled cake and finish with plenty of colorful sprinkles. Let it set before slicing into squares.