In a small bowl, dissolve the cornstarch in ¾ cup water.
In a medium saucepan, combine the coconut milk and sugar, and bring to a boil over medium heat. Add the cornstarch mixture and cook, stirring constantly with a wooden spoon, until the mixture thickens, about 5 minutes.
Pour the pudding into an 8-inch square pan and refrigerate until firm, about 4 hours.
Cut the haupia into squares, and serve. It will keep, well wrapped, in the refrigerator for up to 2 days.