In a medium saucepan, combine the cream, milk, sugar, and salt. Heat over medium until just simmering.
In a separate bowl, whisk the egg yolks. Slowly add some hot cream to temper, whisking constantly.
Pour the yolk mixture back into the pan. Cook on low, stirring constantly, until thick enough to coat the back of a spoon.
Remove from heat. Stir in molasses, anise extract, and black food coloring.
Cool the custard completely, then chill in the fridge for at least 4 hours or overnight.
Churn in an ice cream maker according to manufacturer’s instructions.
Transfer to a container and freeze until firm—about 2-4 hours.