In a medium pot, bring cream, milk, and 1 Tbsp sugar to a boil. Meanwhile, in a large bowl whisk together egg yolks and remaining sugar. Once milk begins to boil, lower heat.
Temper hot milk into sugar-yolk mixture. Slowly add hot milk into yolks about 1/4 cup at a time, whisking to distribute heat. Once all the milk has been added, transfer everything back to the pot.
Stir over medium-low heat until mixture reaches nappe consistency, or 180 degrees F on a kitchen thermometer. Let it sit at 180-185 degrees F for 3 minutes to pasteurize mixture. Remove from heat. Add vanilla and brown sugar. Stir until dissolved.
Transfer to an airtight container. Add cinnamon stick. Let mixture mature in fridge overnight, or for at least 3 hours.
Meanwhile, prepare cinnamon apples. In a medium sauce pot, combine chopped apples, brown sugar, butter and ground cinnamon. Set over medium heat. Let simmer until sugar has dissolved and apples are soft and tender, about 8 minutes. Remove from heat. Add salt and stir. Transfer to an airtight container and let chill in the fridge until ready to use.
Freeze mixture in ice cream maker according to your unit's instructions. Once the volume has increased by half and has reached a soft serve consistency, add prepared cinnamon apple mixture. Continue to churn until apples have been distributed. Transfer ice cream to a freezer safe container. Freeze for at least 30 minutes before serving