In a large mixing bowl, whisk together the milk and sugar until the sugar dissolves.
Stir in the cream and apricot puree. Chill for about an hour.
Meanwhile, combine the chocolate chips and the coconut oil in a microwave-safe bowl. Heat just long enough to melt the chips. Stir until smooth and allow to come to room temperature.
Pour the cream mixture into the ice cream machine and freeze according to the directions provided by the manufacturer of your particular machine. After the ice cream has started to thicken and look like soft serve, drizzle the chocolate mixture into the ice cream. This will harden and break into little "chips" as it churns.
Once the ice cream has thickened, eat immediately as soft serve ice cream or transfer it to an airtight container and store in the freezer for an additional 2 hours or more.
To make the puree: peel, pit, and chop several apricots (how many will depend on their size). Place in a food processor fitted with a metal blade. Puree until smooth. May also be made in a high-speed blender.