1. Make bread pudding: Grease a 9-by-13-inch baking dish with butter. Place bread in prepared pan. Whisk together milk, cream, eggs, egg yolks, granulated sugar, vanilla, salt, cinnamon, allspice, and ginger in a bowl; pour over bread. Let rest, pressing bread down occasionally, 1 hour.
2. Preheat oven to 325°F. Bake until golden brown and cooked through, 35 to 40 minutes. (If you like it a bit darker, increase oven to broil and cook until brown, 1 to 2 minutes.) Transfer to a wire rack, and cool 15 to 30 minutes.
3. Make sauce: Melt butter in a medium saucepan over medium heat. Add brown sugar, salt, and 1/3 cup cream, stirring until smooth. Simmer, without stirring, until sugar melts and mixture looks like caramel sauce, 4 to 5 minutes (reduce heat slightly if it starts to darken too quickly). Remove from heat and carefully stir in bourbon, vanilla, and remaining 1/3 cup cream.
4. Serve bread pudding warm or at room temperature topped with sauce and whipped cream.
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