To infuse the milk, start by pour the milk into a large bowl. Tear 2 of the glazed doughnuts into bite-sized pieces and mix them into the milk. Cover the bowl with plastic wrap and transfer to the fridge for at least 4 hours, ideally overnight. When the milk is done infusing, pour the milk through a sieve, being sure to press the doughnut pieces so they expel any milk. Oh! and you might notice some glaze at the bottom of the bowl; make sure to get all of that too--it's good stuff! The milk should measure out to 1 1/4 cups milk.
To a bowl, prepare an ice bath by adding 10 or so ice cubes and adding a few splashes of water. Set a slightly smaller bowl inside the bigger bowl and set a sieve or strain inside the smaller bowl. Set the whole ice bath contraption aside.
To a medium saucepan, add the infused doughnut-milk, sugar and salt; heat over medium until the milk reaches a slight simmer and the sugar dissolves. Once it reaches the simmer, remove the pan from the heat.
In a medium mixing bowl, beat the egg yolks together, thoroughly. Next you’re going to temper the milk mixture. Whisking the entire time, add about 1/4 cup of warm milk to the egg yolks. Add the remainder of the milk to the egg yolk mixture and whisk. Return the entire mixture back to the medium saucepan and place over low heat. Cook the milk and yolk mixture, stirring constantly, until the thermometer reads 170 to 175 degrees F and the mixture appears thick and coats the back of the spoon.
Pour the mixture through the sieve into the bowl. Stir in the heavy cream. Keep mixing until the mixture is room temperature. Take your last doughnut, break it up into three large pieces and submerge them in the custard mixture. Wrap the bowl in plastic and transfer it to the fridge for 4-5 hours, or overnight, until very cold.
Remove the doughnut pieces from the custard mixture and discard them. Churn the mixture into the bowl of your ice cream maker, according to your ice cream maker’s instructions. Serve immediately for soft serve or alternatively transfer to a freezer-safe container and freeze overnight.
Serve ice cream with a few doughnuts on the side and a sprinkling of sprinkles.