Preheat the oven to 350 degrees Fahrenheit (180 Celsius, or 160 Celsius fan). Grease an 8-inch round cake tin and line the base with a circle of greaseproof paper.
If using a food processor, add the butter, caster sugar, eggs, self-raising flour, milk, and vanilla extract, then blend for one to two minutes until smooth.
If mixing by hand, beat the butter and caster sugar together until combined, then add the eggs one at a time, mixing well after each addition. Fold in the self-raising flour, milk, and vanilla extract until smooth.
Divide the batter evenly between two bowls. Stir the cocoa powder into the batter in one bowl until fully combined, leaving the other bowl as plain vanilla batter.
Using two spoons, dollop spoonfuls of the chocolate and vanilla batters into the prepared tin, alternating between the two so the base is evenly covered.
Tap the tin gently on your work surface to release any air bubbles.
Take a skewer and swirl it through the batter a few times to create a marbled pattern.
Bake for forty five to fifty five minutes, until a skewer inserted into the center comes out clean.
Turn the cake out onto a cooling rack and leave to cool completely before slicing.