For best results, bake your cake the day before you want to make the lamingtons. Cut the cake into 21 squares.
To make the icing, sift your sugar and cocoa into a bowl. Mix in remaining ingredients except coconut and stir until smooth and shiny, using a little more water if necessary to reach the right consistency.
Use immediately, keeping the bowl over hot water. Add a little more boiling water if the icing begins to thicken as you work. Dip the squares of the cake into the icing. A carving fork or skewer is useful. Allow to drop for a minute and then roll in coconut. Leave on a wire rack to dry.
Set your oven temperature to 275 degrees fahrenheit. Place egg whites and a pinch of salt in a bowl and begin to beat until frothy, increasing the speed until they are stiff and dry. Gradually add sugar, while still beating, until the mixture is very stiff and stands in peaks. With a metal spoon, fold in the vinegar and corn starch.
Place a sheet of parchment paper on a sheet pan. Draw a 9-inch circle on the paper, using a 9-inch plate as a guide, then turn the paper over so the circle is on the reverse side. Pile the meringue into the middle of the circle on the parchment paper and smooth it within the circle, making a rough disk. Bake for 1 1/2 hours. Turn off the oven, keep the door closed, and allow the meringue to cool completely in the oven, about 1 hour. It will be crisp on the outside and soft on the inside.
Invert the meringue disk onto a plate and spread the top completely with sweetened whipped cream and cover with your glazed strawberries. Optional: around the holidays you can also sprinkle peppermint chocolate over the top, for an extra minty flavor.