Lightly grease two baking trays.
Cream the butter or margarine with the sugar until very soft, light and fluffy.
Gradually add the egg, beating continuously.
Sift the flour with the cornflour, then work these dry ingredients into the creamed mixture to make a fairly firm dough.
Knead lightly, then roll out the dough on a lightly floured board to a thickness of 3 mm/1/8 in.
Cut into 20 rounds, using a 6.5 cm/2 1/2 in plain cutter.
Carefully sandwich two rounds of biscuit dough with a lollipop stick in between.
Using a palette knife, transfer the biscuits to the prepared baking trays and chill for 30 minutes.
Bake in a moderate oven (180C, 350F, gas 4) for 15 minutes, or until lightly browned.
Remove the hot biscuits from the trays and transfer them to a wire rack to cool completely.
While the biscuits are cooling, make the glace or royal icing, according to the recipe instructions, and four greaseproof paper piping bags (or more, depending on the number of colours you wish to decorate the lollipops with).
Divide half the glace icing into four portions, add a different food colouring to each portion and spoon into the paper piping bags.
Spread each of the cooled biscuits with white icing and apply smarties for eyes.
Snip the ends off the paper piping bags and pipe in hair and features.
Allow the icing to set before serving the lollipops.