Place the plain flour, cornflour and butter in a food processor and blitz until the mixture resembles breadcrumbs. Add the sugar, egg and vanilla extract and pulse again briefly until combined. Remove the dough from the processor and gently knead into a disc. Wrap in clingfilm and chill for 20-30 minutes.
Preheat the oven to 180°C/fan 160°C/gas mark 4. Lightly dust your work surface with flour, then roll out the dough until it’s about the thickness of a £1 coin. Using a 7cm circle cutter, cut as many circles as you can from the dough. Using a smaller circle 3cm cutter, cut a small circle from the centre of each biscuit. Work the scraps into a ball, reroll and cut some more biscuits.
Transfer the biscuits to a baking tray lined with greaseproof paper. Bake in the oven for 10 minutes until they're pale golden. Transfer to a cooling rack and leave to cool completely.
Split the icing into four small bowls with 75g in each bowl. Add 1 tbsp water to each and mix until you have a smooth, runny icing. Colour each bowl of icing with a different colour. Dip each biscuit in a base colour and place on a cooling rack over some greaseproof paper to catch any excess icing. Using a spoon, immediately drizzle the biscuit with an alternate colour in horizontal lines, then use a toothpick to feather the icing, dragging the lines vertically until the icing feathers. Repeat until all the biscuits are all covered. You can vary the base and drizzle colour as you like. Leave to set for 30 minutes before serving or store in an airtight container for 3-4 days.