Cream the butter and sugar in the bowl of an electric mixer, or use a large bowl with a hand-held electric beater. Beat in the vanilla and egg, then add the flour. Beat until smooth, remove from the bowl, halve the dough and beat the cocoa into one of the portions using a mixer. Shape both dough portions into rough oblongs. Wrap in clingfilm and chill for 30 minutes until firm.
Roll out each dough to £1-coin thickness, trying to keep the oblong shape. Put the chocolate dough on top of the white dough and trim the edges to neaten. Roll up lengthways like a Swiss roll, then wrap in clingfilm and chill for 45 minutes. Heat the oven to 180C/fan 160C/gas 4.
Slice the dough into discs as thinly as you can, put them on a non-stick baking sheet and cook for 15 minutes. Cool on wire racks.