Add milk and 1 cup of cream to a medium bowl. Break up 2 doughnuts into tiny pieces and add to the milk and cream. Stir together and cover. Refrigerate for at least 4 hours and up to 24 hours.
Remove chilled doughnut milk mixture from refrigerator. Pour mixture over sauce pan, straining out doughnut pieces and squeezing out all the milk from them. Add sugar, and salt to the sauce pan. Heat until the mixture is steaming, but not boiling. Remove from heat.
Add yolks to a medium bowl and very slowly whisk in warm milk. Transfer mixture back to saucepan and set over medium heat. Stir constantly until mixture thickens slightly and is 170 degrees. Remove from heat immediately so the mixture doesn't scramble.
Place remaining heavy cream in a large bowl and place strainer over bowl. Pour thickened yolk mixture through strainer to remove lumps. Stir with cream. Cover with plastic wrap. Chill mixture until completely cold, about 4-6 hours.
While the mixture chills, prepare the raspberry sauce. Add raspberries and sugar to small sauce pan and place over medium heat. Cook, stirring occassionally, until the mixture thickens up and reaches 220 degrees. Turn off heat and let raspberry sauce cool slightly. Transfer to a storage container, cover, and chill until cold.
Once chilled, ice cream base is ready for your machine. Freeze ice cream according to machine instructions. Cut final doughnut into bite-sized pieces.
Once mixture is frozen, layer ice cream with doughnut pieces and drizzles of raspberry sauce. I did two layers to make sure every bite had tons to raspberry sauce. Cover and freeze ice cream until solid, about 8 hours.