In a medium saucepan over medium heat, bring the milk, cream, salt and ½ cup sugar to a simmer. Whisk until the sugar dissolves, then remove from heat.
In a medium mixing bowl whisk together the egg yolks and remaining sugar until well combined, about 2 minutes. Whisk the egg mixture into the milk mixture in the saucepan.
Return the pot to medium heat and cook, stirring constantly until the mixture is thick enough to coat the back of a spoon, about 2 to 3 minutes.
Strain the custard through a fine mesh sieve into a medium bowl set in a large bowl of ice water. Let the mixture cool, stirring occasionally.
Add the custard to the chilled bowl of an ice cream maker set up according to manufacturer's instructions. Mix for about 12 minutes then add the fig jam.
Continue to mix until the consistency is thick, about an additional 15 to 20 minutes. Drop in the balsamic and swirl into the mixture with a spatula.
Use a rubber spatula to transfer the ice cream to an airtight container, cover and freeze until firm, at least 4 hours. The ice cream can be kept frozen for up to 1 week.