In a medium pot, bring cream, milk, and 1 Tbsp of sugar to boil. Meanwhile, in a large bowl whisk together egg yolks and remaining sugar. Once milk begins to boil, lower heat.
Temper hot milk in sugar-yolk mixture. Slowly add hot milk into yolks about ¼ cup at a time, whisking to distribute heat. Once all the milk has been added, transfer mixture back into the pot.
Stir over low-medium heat until mixture reaches nappe consistency, or 180°F on a kitchen thermometer. Remove from heat and stir in vanilla. Transfer to an airtight container and let mixture mature in fridge overnight.
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 crushed candy cane. Continue to churn until candy cane has been distributed. Transfer ice cream to a freezer safe container. Freezer for at least 1 hour before serving.