In a medium saucepan, combine heavy cream, whole milk, brown sugar, ground cinnamon, and a pinch of salt. Heat over medium heat, stirring frequently until the mixture is hot and the sugar has completely dissolved—about 5 minutes.

Place the egg yolks in a separate medium bowl and whisk them until smooth and slightly pale in color.

Once the cream mixture is hot, gradually pour about one cup into the whisked egg yolks while constantly whisking.

Return the tempered yolk mixture back to the saucepan with the remaining cream mixture. Stir continuously over medium-low heat until the custard thickens enough to coat the back of a spoon, about 5 to 7 minutes.

Strain the custard through a fine-mesh sieve into a clean bowl to remove any small bits of cooked egg. Stir in the vanilla extract while the mixture is warm.

Allow the strained mixture to cool to room temperature, about 30 minutes.

Cover the bowl with plastic wrap and refrigerate the mixture for at least 4 hours, or preferably overnight.

Churn the custard in an ice cream maker according to the manufacturer's instructions until it reaches a soft-serve consistency, about 20 to 25 minutes.

Transfer the churned ice cream to a freezer-safe container, spreading it evenly, and freeze for several hours until firm.

Serve your creamy brown sugar cinnamon ice cream in bowls or cones, optionally sprinkling with extra cinnamon.