Spray a 9" x 2" cake pan with pan spray. (See Notes for Springform directions) Line the bottom with a circle of parchment paper.
Cut some of the doughnuts in half and some in quarters. Fill the pan with the halves, packing them in snugly. Fill in with quartered doughnuts. Again, they should fit snugly.
Take a wooden skewer and pierce the doughnuts all the way through all over. Tons and tons of tiny holes will help the custard soak in so you don't have any pockets of dry doughnut in your delicious, soft, custardy bread pudding.
Slowly pour all the custard into the middle of the pan. Allow to sit at cool room temperature for 30 minutes.
Place a piece of plastic wrap on top of the doughnuts and then place a plate on top of that. Use a couple of cans as weights so the plate presses down on the pudding, compacting all the doughnuts and helping the custard soak in. Refrigerate overnight or allow to sit at cool room temperature for another 90 minutes or so.
Test to make sure all the doughnuts are saturated by sticking a skewer in. There should be almost no resistance.
About 30 minutes before you're ready to bake, heat the oven to 300F.
When time to bake, place the bread pudding on the center rack and bake until the pudding is well risen all over and lightly golden brown on top. This will take about an hour. The internal temperature in the center of the pudding should be 175-180F.
Remove from the oven and allow to cool in the pan for an hour.
Run a thin spatula around the inside of the pudding to release it in case it stuck at all.
Cover a large cake circle or flat plate with plastic wrap. Place on top of the cake pan and invert the whole shebang. Give it a shake so the parchment releases from the bottom of the pan. Peel off the parchment, cover the cake either with the pan it just came out of or with more plastic wrap. Chill until cold.
Remove from the fridge 2 hours before serving. You want it to temper for an hour, then the glaze needs a good 30 minutes to set up and then you have to warm up the pudding (it's fine cold, but it's dreamy warmed up).