Combine turbinado or light brown sugar, egg yolks, and salt in a 3-quart stainless steel saucier, then whisk in cream and milk. Cook over medium-low heat until warm to the touch, then increase to medium and cook, stirring constantly with a flexible spatula, until mixture is steaming-hot but not bubbling, about 8 minutes or to 155°F (68°C) on a digital thermometer. Off heat, whisk in black sesame paste and strain mixture through a fine-mesh sieve into a large stainless steel bowl. For a more homogeneous color, process about 30 seconds with an immersion blender; this is strictly an aesthetic consideration.
Fill a sink compartment or extra-large bowl with a few inches of ice water and place bowl of custard inside, stirring from time to time, until cool, about 30 minutes. Cover and refrigerate until no warmer than 40°F (4°C), about 4 hours, or hold up to 1 week.
Churn in an ice cream machine according to the manufacturer’s directions. Meanwhile, place a 1-quart container and flexible spatula in the freezer. When ice cream is fluffy and thick, shut off the machine and scrape ice cream into chilled container, using chilled spatula. Enjoy as soft-serve or cover with plastic pressed directly against surface of ice cream, then close lid and freeze until hard, about 4 hours.