1. Combine 1/2 cup of the milk and half the coconut in an electric blender container; blend well. Add an additional 1 1/2 cups milk; blend 5 minutes. Strain out coconut pieces through a double thickness of cheesecloth. Repeat blending and straining, using remaining coconut and milk.
2. Mix cornstarch with sugar in a saucepan. Gradually add the coconut milk, stirring until smooth. Bring rapidly to boiling and cook 2 to 3 minutes, stirring constantly.
3. Pour into a buttered 8-inch square pan; cool. Refrigerate until firm. Cut into rectangle.