In a medium saucepan, combine 2 cups of heavy cream, 1 cup of whole milk, 1 cup of brown sugar, 2 teaspoons of cinnamon, and a pinch of salt over medium heat until hot and sugar dissolves.

Whisk 5 large egg yolks in a separate bowl until smooth and pale, about 2-3 minutes.

Gradually drizzle 1 cup of the hot cream mixture into the egg yolks while whisking continuously.

Pour the egg yolk mixture back into the saucepan and cook over medium-low heat, stirring constantly until the custard thickens, about 5-7 minutes, ensuring it doesn't boil.

Strain the custard through a fine-mesh sieve into a clean bowl to eliminate cooked egg bits.

Stir in 1 teaspoon of vanilla extract and allow the mixture to cool for about 30 minutes. Refrigerate for at least 4 hours or overnight.

Churn the chilled custard in an ice cream maker according to the manufacturer's instructions for 20-25 minutes.

Transfer to a freezer-safe container, smooth the top and freeze for at least 4 hours until firm.