Brush bottom and sides of a 13 x 9 baking dish with coconut oil or melted butter. Set aside
In a large pot, combine coconut milk, evaporated milk, condensed milk, and sugar.
Bring to a gentle boil, stirring regularly, until sugar is dissolved.
Add 2 cups of the fruit cocktail and stir to distribute. Cook for about 1 to 2 minutes.
In a small bowl, combine water and cornstarch. Stir well until cornstarch is dissolved.
Gently add cornstarch mixture into milk mixture, whisking vigorously to prevent lumps. Continue to cook, whisking continuously, until mixture thickens to a thick paste.
Transfer mixture into the prepared dish, smoothing top with a lightly oiled spatula or knife.
While still warm garnish top with the remaining 1/2 cup fruit cocktail.
Allow to slightly cool, cover and refrigerate for about 1 to 2 hours or until completely cooled and set.
Sprinkle top with shredded cheese and cut into serving pieces.