In a medium saucepan, combine the heavy cream, milk, egg yolks, sugar, and vanilla. Bring to a steep over low-medium heat. Steam should begin to rise from the liquid. Stir consistently and continue to cook over low-medium heat for approximately 8 to 10 minutes until the custard slightly thickens. The custard should lightly coat the back of a spoon when ready.

Transfer the custard to a bowl to cool and cover with plastic wrap. The plastic wrap should touch the top of the custard to prevent a skin from forming. Place the container in a large bowl of ice to chill for about 1 hour, then transfer to the refrigerator to cool completely, about 2 hours.

After the custard cools, pour it into the prepared ice cream maker. Churn according to manufacturer’s instructions until the ice cream reaches the soft set stage. Add the key lime juice. Continue to churn until the ice cream is well mixed and has begin to set.

Transfer the ice cream to a freezer safe container, and place in the freezer until completely firm. This will vary based on how frozen the ice cream is when it’s removed from the ice cream maker. (Ours took 8 to 10 hours.)

Allow the ice cream to set out at room temperature for about 10 minutes before scooping. Serve cold.