Heat the Milk and Cream: In a saucepan over medium heat, combine the milk, heavy cream, granulated sugar, and brown sugar. Stir occasionally until the mixture is hot but not boiling.

Prepare Egg Yolks: In a separate bowl, whisk the egg yolks. Slowly add a little of the hot milk mixture to the yolks to temper them. Gradually whisk in the rest of the hot mixture.

Cook the Custard: Return the mixture to the saucepan and cook over medium heat, stirring constantly until it thickens and coats the back of a spoon. This should take about 10 minutes.

Add Coffee and Chill: Remove from heat and stir in the cold brew coffee, vanilla extract, and salt. Strain the mixture through a fine-mesh strainer into a clean bowl. Cool to room temperature, then refrigerate for at least 4 hours or overnight.

Churn the Ice Cream: Once chilled, pour the mixture into an ice cream maker and churn according to the manufacturer’s instructions, usually about 15 minutes.

Freeze: Transfer the churned ice cream to a container and freeze for at least 2 hours to firm up before serving.