Grease 2 baking sheets. To make the dough put the butter and flour in a food processor and blend until the mixture resembles breadcrumbs. Add the sugar, egg yolks and vanilla and blend to a smooth dough. Wrap in clingfilm and chill the dough for at least 1 hour.
Roll out on a lightly floured surface and cut out rounds with a 10 cm (4 inch) cutter, rerolling the trimmings making 20. Cut each round in half and bake on baking sheets, in a preheated oven, 180°C (350°F), Gas Mark 4, for 15 minutes, until pale golden. Transfer to a wire rack.
Knead the green icing a little on a surface lightly dusted with icing sugar. Tear the yellow icing into pieces and dot over the green icing. Roll the lump of icing with your hands into a thick sausage. Fold it in half and roll again. Repeat rolling and folding until the colours have marbled together. Beat together the icing sugar and butter with the water until smooth and creamy. Put the buttercream in a piping bag with a fine plain nozzle. Roll out the marbled icing thinly. Lay a cookie over the icing and, using a small, sharp knife, cut around it, adding an icing tail.
Pipe buttercream over the cookie and lay the marbled icing on top. Repeat with the rest of the cookies. Reroll the icing trimmings and cut out small heads, marking mouths with a knife. Secure to the bodies with frosting. Shape and secure ears and feet. Cut the chocolate buttons into triangles and, using buttercream, secure along the top of each 'body', making the triangles smaller at the tail end. Pipe eyes and claws with buttercream. Shape and secure balls of brown icing for the centres of the eyes.