Preheat the oven to 180ºC, fan 160ºC, gas 4. Grease and line a 20cm x 20cm square cake tin.
In a medium bowl, cream together the butter and sugar until light and fluffy. Whisk in the eggs, 1 at a time, with a spoonful of the flour – this will stop the mixture from splitting. Fold in the remaining flour and vanilla essence.
Divide the mixture between 2 bowls. Gently fold the jam, red food colouring and raspberries through the mixture in 1 of the bowls until smooth, and fold the milk through the other. Spoon the batters into the prepared tin in 2 layers, alternative spoonfuls of raspberry and vanilla to simulate a checkerboard. Tap the bottom of the tin on a work surface to ensure there aren't any air bubbles. To create marbling, run a table knife (or wooden skewer) through the batters in a swirling motion.
Bake for 40-45 minutes or until a skewer inserted into the centre comes out clean. Turn out onto a cooking rack and leave to cool completely. Dust with the icing sugar and cut into squares (they'll keep in an airtight container for up to 3 days).