In a large bowl, whisk together the eggs, heavy cream, milk, sugar, vanilla extract, cinnamon, and salt until smooth.
Arrange the bread slices in a shallow dish and pour the custard mixture over them, making sure all slices are evenly coated. Let soak for 20–30 minutes.
Melt the butter in a skillet or baking dish over medium heat, then sprinkle sugar evenly over the butter to create a caramel base.
Place the soaked bread slices over the caramel base and cook or bake until the custard is set and the bottom is golden.
Sprinkle sugar over the tops of the toast and caramelize using a kitchen torch or under a broiler until crisp.
Serve immediately while warm and crunchy.