This pudding is so delicious and so creamy, it's hard to believe that it's both non-dairy AND oil free!!! It's an old standby and one of my favorites, quick and easy, and nice for when you're craving something sweet. It's from the book, "150 Vegan Favorites", by Jay Solomon (ISBN 0761512438), page 229.
Haupia (Hawaiian Coconut Pudding)
¼ cup sugar
¼ cup cornstarch
1½ cups (12 oz.) canned coconut milk
1 tablespoon vanilla extract
*I also add ½-1 teaspoon of salt
In a small bowl, combine the sugar and cornstarch (and salt, if using) and set aside. In a small sturdy saucepan, combine the coconut milk and vanilla extract and bring to a gentle simmer over medium heat, stirring frequently. Freduce the heat to low and cook, stirring, for 4-5 minutes. Whisk the sugar mixture into the coconut milk and cook, stirring, until the mixture thickens (like pudding), about 3-4 minutes. Remove the pan from heat. Pour the pudding into an 8"x8" square pan, lightly cover, and refrigerate until firm, about 2-3 hours. Cut the pudding into small squares and serve. Yield: 6-8 servings
Here's a helpful tip (and another recipe for haupia) from this website:
"If the haupia is grainy, you need to keep cooking the mixture because the fat in the coconut milk has not yet melted."