Place milk, 1 cup of cream, sugar, and salt in a medium 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. Add vanilla extract and almond extract. Cover with plastic wrap.
Chill mixture until completely cold, about 4-6 hours. Once chilled, ice cream base is ready for your machine. Freeze ice cream according to machine instructions. While the ice cream freezes, mix all the ingredients together for the cream cheese frosting. Whisk to ensure there are no lumps.
Once mixture is frozen, layer ice cream with cake pieces and drizzles of cream cheese icing. I did two layers to make sure every bite had tons to cake. Freeze ice cream until solid, about 8 hours.