For the bread pudding: Preheat the oven to 350 degrees F. Grease the bottom and sides of a deep 13-by-9-inch baking dish with the butter. Set aside.
In a large bowl, whisk together the heavy cream, sour cream, maple syrup, brown sugar, cinnamon and salt until smooth. Whisk in the eggs, one by one, until the custard is smooth. Stir in the bread cubes and let soak for at least 10 minutes.
Pour the custard-bread mixture into the prepared baking dish and bake until golden brown on top and the custard is set, 35 to 40 minutes. Let cool completely. Leave the oven on.
For the meringue: Whisk the egg whites and salt until light and frothy in a stand mixer fitted with the whisk attachment. Add the cream of tartar. Slowly add the granulated sugar, a little at a time, whisking until the egg whites have quadrupled in size and are stiff and shiny.
Finish the bread pudding: When the bread pudding is cool to the touch, stir to break it apart and then stir in the butterscotch and chocolate chips to evenly distribute them. Transfer one-third of the meringue to the bread pudding and fold it in until incorporated. Using the back of a spoon, spread the pudding into an even layer in the baking dish. Pipe the rest of the meringue on top in decorative peaks.
Bake until golden brown and cooked through, another 30 to 35 minutes.
For the bourbon sauce: Melt the ice cream in a small saucepan over medium heat. Stir in the bourbon and nutmeg. Pour into a sauce dish and ladle over each serving of bread pudding.