Adjust oven rack to middle position and heat oven to 375. Whisk milk, eggs, 4 T sugar, pudding mix, vanilla and salt in large bowl til combined. Stir in bread. Let stand, tossing occasionally, until liquid is absorbed, about 10 minutes.
Combine cinnamon and remaining sugar in small bowl. Grease 8" square dish. Transfer bread mixture to prepared pan and sprinkle with cinnamon sugar. Bake until pudding is just set and surface is golden brown, 35-40 minutes. Let cool 30 minutes.