Heat the oven to 350 degrees. Butter a 9-inch square baking dish.
In a large bowl, beat together the eggs and egg yolks until completely combined. Whisk in 1 cup/240 milliliters heavy cream, 3/4 cup/180 milliliters condensed milk, (reserve remainder of heavy cream and condensed milk ) 1 cup whole milk, 1 cup evaporated milk, vanilla and salt.
Set the bread in the prepared dish and pour the egg mixture on top. Press the bread down gently with a spatula to make sure all the pieces are immersed and soak up the liquid. Let stand at room temperature for 10 minutes.
Meanwhile, bring a kettle of water to a boil. Drizzle 2 tablespoons condensed milk over the pudding. Cover the baking dish tightly with aluminum foil then set it inside a large roasting pan. Pour the boiling water into the roasting pan until it reaches about halfway up the sides of the baking dish.
Bake until the center of the custard is almost set but still slightly wet, about 25 minutes. Carefully remove the foil and continue to bake until the custard is set in the center and the top is golden, about 30 minutes longer. Carefully remove the roasting pan from the oven and let the pudding cool in the water for about 20 minutes.
Whip the remaining 1 cup/240 milliliters heavy cream to soft peaks. Serve the pudding warm, room temperature or cold with a dollop of whipped cream. Drizzle with the remaining 2 tablespoons condensed milk.
