Preheat the oven to 350 degrees F. Butter a 2-quart baking dish.
In a large bowl, whisk together the cream, milk, egg and yolk mixture, brown sugar, vanilla, and salt. Make sure the mixture is well combined.
Add half of the brioche to the prepared baking dish, and sprinkle evenly with half of the raspberries and chocolate. Top with the remaining brioche, raspberries, and chocolate.
Pour the cream mixture over the brioche mixture. Press down gently, cover it with plastic wrap, and let stand for 30 minutes. You want the bread to soak up that luscious custard.
Bring a kettle of water to a boil. Remove the plastic wrap and set the baking dish in a large roasting pan. Fill the roasting pan with enough boiling water to get about halfway up the sides of the baking dish. Carefully place the pan in the oven and bake until the custard is set (even in the very center), and the bread has puffed, 50 to 60 minutes. Let cool slightly and remove the baking dish from the water. Serve warm, room temperature, or chilled.