Cut the doughnuts into 6 pieces. Add to a greased 9x13" baking dish.
Add the eggs, milk, sweetened condensed milk, brown sugar, salt, vanilla, cinnamon and nutmeg to a medium mixing bowl and mix well with a whisk.
Pour over the doughnut pieces.
Use the back of a spoon to push down the doughnuts into the custard mixture. Allow to sit and rest and soak up the milk mixture. Turn on oven to 350°F.
After about 30 minutes place the baking dish into the oven and bake uncovered for about 40-45 minutes. Until golden brown on top.
While the bread pudding is baking add the ingredients for the vanilla sauce to a small sauce pan and heat til almost boiling point. Stirring constantly.
Remove the bread pudding when ready. Slice after about 15-20 minutes, after it has cooled somewhat.
Slice and serve with a drizzle of the vanilla sauce.
Notes
The longer you can leave the doughnuts soaking in the custard mixture, the better.For best results try to make sure the doughnuts have had time to become stale.