Preheat the oven to 350 degrees.

Spread the bread cubes on a rimmed baking sheet, place in the oven, and toast until golden brown, 8 to 10 minutes. Remove the bread cubs from the oven but leave the oven on.

Generously spray a 12-inch round ovenproof pan or a 3-quart baking dish with nonstick spray. Transfer the bread cubes to the pan, spreading them evenly.

In a large saucepan, combine the milk, cream, and sugar evenly over medium heat and bring to a simmer, stirring to dissolve the sugar. Stir in the vanilla and remove from the heat.

In a medium bowl, whisk together the eggs, egg yolks, and salt. Slowly pour 1/2 cup of the hot milk mixture into the eggs while whisking the milk mixture int the pan continuously, carefully pour the egg mixture into the pan, using a rubber spatula to scrape every bit from the bowl.

Pour the custard mixture evenly over the bread cubes and let stand at room temperature for 5 minutes. Then, using the spatula or the back of a large spoon, gently press the bread down into the custard mixture. Sprinkle the white chocolate chips evenly over the top, and fold them gently into the bread mixture. Evenly spread the berries and/or cherries on top.

Place the baking dish inside a larger roasting pan. Open the oven door, pull out the center rack most of the way, but not so far that it will tip when the pan is set on it. Set the roasting pan holding the baking dish on the rack, and then pour hot water into the roasting pan to reach about halfway up the sides of the baking dish. Slowly slide the rack into the oven and close the oven door. Bake until the pudding appears just set in the center when the baking dish is gently jiggled and the top is beginning to color, about 45 minutes.

Remove the roasting pan from the oven, being careful to avoid splashing the water, and lift the baking dish out of the pan. Serve the pudding hot, warm, or at room temperature.