Coat a 9 by 13 inch baking dish with cooking spray.
Cut the doughnuts into 1.5 inch pieces. Place in the baking dish.
Whisk together the remaining ingredients in a large bowl. Pour into the dish over the doughnuts. Let sit at room temperature for 20 minutes.
Preheat oven to 325F.
Bake the pudding on the lower middle rack until it is golden brown and puffing up around the edges, with a slight jiggle in the middle, approximately 45-50 minutes.
Let cool for 30-45 minutes before serving warm. Top with caramel, sprinkles, or other sauces if desired. This pudding is great served with whipped cream or ice cream.
Notes
You can let the doughnuts soak in the refrigerator for up to 24 hours if needed.