Whisk eggs, milk, and salt together in a bowl; pour into a shallow dish. Soak bread slices in egg mixture until saturated.
Spread softened butter over the bottom of a 10x15-inch jelly roll pan. Sprinkle brown sugar over the butter. Arrange bread slices onto sugar in a single layer; sprinkle with cinnamon.
Bake in preheated oven until beginning to firm, 25 to 30 minutes.
