In a medium saucepan, mix heavy cream, whole milk, brown sugar, cinnamon, and salt. Heat until warm, ensuring the sugar dissolves without boiling.

In a separate bowl, whisk the egg yolks until smooth. Gradually add 1 cup of the warm cream mixture to temper the eggs.

Pour the yolk mixture back into the saucepan. Cook over medium-low heat, stirring continuously until thickened, reaching a temperature of 170°F to 175°F.

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

Stir in vanilla extract, then let cool to room temperature. Cover and refrigerate for at least 4 hours or overnight.

Once chilled, pour the custard into an ice cream maker and churn until soft-serve consistency.

Transfer churned ice cream to a freezer-safe container and freeze for several hours until firm.