For the vanilla sauce: Bring the milk and salt to a simmer over medium heat in a 2-quart heavy saucepan. Whisk together the yolks and sugar in a bowl until combined, and then add to the hot milk in a slow stream, whisking. Transfer the custard back to the saucepan and cook over moderately-low heat, stirring constantly with a wooden spoon, until the custard coats back of a spoon, about 5 minutes. Pour through a fine-mesh sieve into a bowl and stir in the vanilla. Cover the surface of the custard with a round of wax paper and chill until cold, at least 1 hour.
For the bread pudding: Preheat the oven to 325 degrees F. In large mixing bowl, toss together the donut slices, dried cherries and white chocolate. Set aside. In second large mixing bowl, stir together the sugar, cinnamon and nutmeg. Measure out 1/4 cup of spiced sugar into a small bowl and set aside.
In a third large mixing bowl, whisk together the eggs, cream, milk and vanilla. Whisk the eggs into the large bowl of spiced sugar, and then pour over the bread-chocolate mixture and stir to combine. Pour the batter into a 9-by-13-by-2-inch baking pan and sprinkle with the reserved 1/4 cup spiced sugar. Scatter the butter cubes over top and bake until golden brown and just set in middle, 50 to 60 minutes.
Serve with the vanilla sauce.