In a medium saucepan, combine heavy cream, whole milk, brown sugar, cinnamon, and a pinch of salt over medium heat. Stir until hot and sugar is dissolved.

Whisk together egg yolks in a medium bowl until smooth and slightly pale.

Gradually drizzle hot cream mixture into the whisked yolks while continuously mixing to temper yolks.

Pour the tempered egg yolk mixture back into the saucepan with the remaining cream mixture and cook over medium-low heat until thickened.

Strain the custard through a fine-mesh sieve into a clean bowl to ensure smoothness.

Stir in vanilla extract and let the mixture cool. Refrigerate for at least 4 hours or overnight.

Churn the cooled custard in an ice cream maker according to manufacturer's instructions.

Transfer churned ice cream to a freezer-safe container and freeze for at least 4 hours.