Chop the chocolate if using a bar, place it in a large bowl, and set it aside.
Add the coconut milk, sugar, milk and pinch of salt to a 2 or 3 quart saucepan.
Make a slurry by stirring the cornstarch into the water. It will settle quickly, so make sure it is stirred up, then add it to the coconut milk mixture and cook immediately.
Cook on medium heat until the haupia is very thick. If you have a digital or cooking themometer, the haupia will thicken at about 170F (77C). Cook while thickened for 1-2 minutes, then remove the pan from the heat.
Immediately pour 1/3 of the haupia into the bowl with the chocolate. Allow it to sit on top of the chocolate for 30-60 seconds before stirring, to ensure the chocolate melts well. Stir, and once the chocolate is fully incorporated, spread the chocolate on top of the shortbread in the 8x8 pan for the second layer.
Spoon the rest of the haupia over the chocolate layer, then use a spoon or spatula to gently spread it across the chocolate for the top layer.
Chill at least 4 hours before serving.