Beat the butter until light and creamy. Add the powdered sugar and beat until combined. Add the cornstarch, plain flour and vanilla, and mix at slow speed until just blended together. For firmer biscuits, add extra flour at this stage.
Lightly butter and flour a baking tray and preheat the oven to 325°F
Make a ball from a level dessert spoon of the mixture and place on the tray, allowing room for the biscuits to spread. Repeat with remaining mixture.
Dip a fork into some flour, knocking off any excess and make an imprint with the tines, flattening the biscuits a little.
Place the tray on the centre shelf of the oven and bake slowly until the biscuits are just coloured, 10 to 15 minutes.
Remove from the oven with a spatula and place the biscuits on cake rack.
To make icing:
Beat the butter with a wooden spoon. Add the powdered sugar and beat until the sugar is almost absorbed with the butter. Add the vanilla and salt and with the addition of a little boiling water, bring to a thick and creamy consistency, balancing with a little more powdered sugar if necessary.
To finish the biscuits, join 2 biscuits together with a tsp of icing spread with a knife. Return to a cooling rack until the icing is completely set before removing to an airtight container.