Creamy Caramel Pudding

Combine 1/2 cup milk, cornstarch, vanilla and salt in a small bowl and whisk until smooth. Combine the sugar and water in a large saucepan over medium high heat. Cook, stirring, until the sugar dissolves. Continue cooking, without stirring, about 8 minutes until a deep amber color forms. Remove the pan from the heat and whisk in the remaining milk 1/4 cup at a time. Place the pan over medium heat and whisk until the caramel dissolves. Reduce the heat to medium low and cook about 10 minutes until slightly thickened. Remove the pan from the heat and whisk in the cornstarch mixture. Cook the pudding over medium heat until very thick, stirring constantly. Strain the pudding. Cover and refrigerate the pudding at least 2 hours until well chilled.