Bring milk, cream, salt, and ½ cup sugar just to a simmer in a medium saucepan, stirring to dissolve sugar; remove from heat. Whisk egg yolks and 2 Tbsp. sugar in a medium bowl until pale, about 2 minutes. Gradually whisk ½ cup hot milk mixture into yolks. Whisk yolk mixture into remaining milk mixture in saucepan. Cook over medium heat, stirring constantly, until thick enough to coat the back of a wooden spoon, 2–3 minutes. Strain custard through a fine-mesh sieve into a medium bowl set in a large bowl of ice water; whisk in flavored olive oil. Let cool, stirring occasionally. Process custard in an ice cream maker according to manufacturer’s instructions. Transfer ice cream to an airtight container, cover, and freeze until firm, at least 4 hours.
Makes about 3½ cups
DO AHEAD: Ice cream can be made 1 week ahead. Keep frozen