Prepare the Custard Base: In a medium-sized, heavy-bottomed saucepan (about 3 quarts), combine the sugar, egg yolks, and salt. Whisk well until the mixture becomes pale and smooth. Gradually pour in the heavy cream and milk while whisking continuously to fully incorporate the ingredients.
Heat and Thicken the Mixture: Set the pan over medium-low heat and cook gently, stirring constantly with a heat-resistant spatula to prevent sticking. Once the mixture feels warm to the touch, increase the heat slightly and continue stirring until it reaches about 155°F (68°C) or is steaming hot but not bubbling. The custard should lightly coat the back of a spoon.
Add the Sesame Flavor: Remove the pan from the heat and immediately whisk in the black sesame paste until fully blended and smooth. Strain the mixture through a fine-mesh sieve into a large, heat-safe bowl to eliminate any small lumps or curdled bits. For an extra silky, uniform texture and darker color, blend the mixture briefly with an immersion blender.
Cool the Custard: Prepare an ice bath by filling a sink or large bowl with cold water and ice. Place the bowl of custard into the bath and stir occasionally until it cools to room temperature, about 30 minutes. Once cooled, cover the bowl and refrigerate for at least 4 hours, or ideally overnight, until the custard reaches 40°F (4°C) or colder.
Churn the Ice Cream: Once the mixture is thoroughly chilled, pour it into your ice cream maker and churn according to the manufacturer’s instructions. While churning, place a clean 1-quart container and a flexible spatula in the freezer to prepare for storage.
Freeze and Set: When the ice cream reaches a thick, soft-serve consistency, transfer it into the pre-chilled container using the cold spatula. Press plastic wrap directly onto the surface to prevent ice crystals, seal with a lid, and freeze for at least 4 hours until firm.