Preheat the oven to 375°F. If not already cubed, cut 1 1/2 loaves aged white bread into 1 1/2-inch cubes and place the cubes in a large bowl.
In a large bowl, whisk together 4 cups heavy cream, 3 cups granulated sugar, 1 egg, and 1 teaspoon vanilla extract until the sugar begins to dissolve. Pour this cream mixture over the bread cubes and toss gently to coat all cubes. Let the bread soak for 30 minutes, stirring gently every 5 minutes to ensure even soaking.
While the bread soaks, make the raspberry filling: in a medium bowl combine 5 cups raspberries (fresh or frozen), 1 cup granulated sugar, and 1/2 cup apple juice. If using frozen raspberries, thaw and drain any large excess liquid before combining. Stir until the sugar is dissolved and set aside.
Assemble the pudding in a 9x13-inch baking dish: spread about 3/4 of the soaked bread mixture evenly into the dish and press down lightly. Spoon the raspberry filling evenly over the bread layer. Top with the remaining bread mixture, spreading to cover the raspberries.
Bake the assembled pudding in the preheated 375°F oven for 40 minutes, or until the pudding is set and the top is lightly browned.
While the pudding bakes, make the vanilla sauce: in a medium saucepan over medium heat melt 1 1/3 cups unsalted butter. Whisk in 5 tablespoons flour and cook, stirring constantly, about 2–3 minutes until the mixture is fragrant and cooked through but not browned. Gradually whisk in 3 cups heavy cream and 1/3 cup granulated sugar. Bring to a gentle simmer and cook, stirring frequently, until the sauce thickens and coats the back of a spoon, about 5–8 minutes. Remove from heat and stir in 2 teaspoons vanilla.
Remove the bread pudding from the oven and let it cool for 10–15 minutes.
Serve the bread pudding warm and spoon the vanilla sauce over each portion.