Butter an 8x8 inch glass baking dish. Soak bread in hot milk for five minutes. Stir in 3/4 cup sugar, 1 tablespoon butter, salt, eggs, and 1 teaspoon vanilla. Pour into the baking dish.
Line a roasting pan with a damp kitchen towel. Place baking dish on towel inside roasting pan, and place roasting pan on oven rack. Fill roasting pan with boiling water to reach halfway up the sides of the baking dish. Bake for 60 minutes. Cool on wire rack.
While pudding cools, combine 1 cup sugar, 1/2 cup butter, cream, and 1 teaspoon vanilla in a large saucepan. While stirring, bring to a boil. Reduce heat to low, and stir 3 minutes more. Spoon over warm bread pudding.