Line a couple of baking sheets with baking parchment.
Cream the butter, sugar and vanilla together in a large bowl until smooth. Don't beat the mixture for too long, you don't want to incorporate too much air.
Add the flour, cornflour and a pinch of salt and mix to form a smooth dough. It may seem crumbly at first but keep mixing and it will come together. If the dough seems very soft then you can add an extra 25g of flour.
If the dough feels too soft to roll out, wrap it and chill it in the fridge for 30-60 minutes until it has firmed up a bit.
Roll half of the dough out on a lightly floured surface to about 4mm thick and use a fluted 6 cm/2 ½ in round cutter to cut out as many rounds as possible. Bring together the scraps and re-roll to cut out more cookies. Repeat with the other half of the dough.
Use a palette knife to lift the biscuits and place them slightly spaced apart on the lined baking sheets; place them in the freezer for 15 minutes or in the fridge for 20. Meanwhile, preheat the oven to 160℃/140℃ fan/320℉/gas mark 3.
Bake the biscuits for 25 minutes until pale golden. Allow to cool on the baking sheets for a minute or two then carefully transfer to a wire rack and leave to cool completely.
To make the icing, gradually stir enough water or lemon juice into the icing sugar to form a thick but spreadable icing.
Spread a small spoonful of the icing over the top of half of the biscuits and press half a glace cherry into the top of each one before the icing sets. Spread about ½ teaspoon of jam over the underside of the other half of the biscuits. Place the iced biscuits on top of the jam covered ones, pressing them down gently.