In a small saucepan over medium heat, combine the butter and brown sugar until melted and smooth. Stir until smooth and caramel-like. Pour this mixture into a greased 9×13 baking dish, spreading it evenly.
Place the thick slices of brioche bread over the caramel layer, overlapping them slightly if needed.
In a large mixing bowl, whisk together the eggs, heavy cream, vanilla, and salt until fully blended.
Gently pour the custard mixture over the bread, ensuring every slice is thoroughly soaked.
Wrap the dish securely with foil or plastic wrap and chill it in the refrigerator overnight.
When ready to bake, preheat your oven to 350°F (175°C). Uncover the dish and place it in the oven. Bake for about 35 to 40 minutes, until golden brown and set in the middle.
Allow the dish to rest for 5 to 10 minutes before serving.
