In a small bowl, stir together corn flour and 1 cup milk.

In a saucepan over high heat, stir together 3 cups milk, sugar, and vanilla. Bring to a boil. Stir the corn flour and milk mixture into the saucepan. Reduce the heat to low, and allow to cool slightly; then stir in cream, stirring constantly until the cream is thickened. Allow to cool momentarily, then pour into individual bowls or one large serving bowl. Sprinkle pistachio nuts on top. Cover, and refrigerate.

To make the syrup, stir together water, sugar, and lemon juice in a saucepan set over high heat. Bring to a boil. Place cinnamon sticks in saucepan, and boil about 5 minutes. Strain liquid, and pour into a bowl. Allow to cool; cover, and refrigerate.

Serve puddings cold with cold syrup drizzled over the top.