To prepare the pudding, combine the first 9 ingredients in a large bowl, and stir well with a whisk. Add bread cubes, and toss gently. Cover bread mixture, and chill 1 hour.
Preheat oven to 350°.
Spoon the bread mixture into an 11 x 7-inch baking dish coated with cooking spray. Bake bread mixture at 350° for 45 minutes or until set.
To prepare the sauce, combine 1 cup low-fat milk and cornstarch in a small bowl. Combine 1/2 cup granulated sugar and butter in a medium saucepan over medium heat. Add the low-fat milk mixture, and bring to a boil. Cook mixture until thick (for about 4 minutes), stirring constantly. Remove from heat, and stir in the rum.