Stir together the Nutella, sugar, and salt in a mixing bowl. Stir in the cream and whisk smooth. Slowly add the milk and vanilla, whisking until smooth. Pour into the ice cream machine and freeze according to the manufacturer's directions.
While the ice cream is churning, warm ⅓ cup Nutella and the coconut oil in the microwave for about 30 seconds. Stir until smooth and liquid. Set aside.
When the ice cream finishes churning, transfer about a third of the ice cream to an airtight container and drizzle with some of the liquid Nutella. Repeat the layers and swirl with a knife just a couple of times to mix throughout.
Cover with a lid and place in the freezer until firm enough to scoop. For an even more amazing treat, drizzle with Nutella hot fudge when serving.
Notes
I usually figure a batch of homemade ice cream to be 5-6 servings. However, this is very rich ice cream and we tend to enjoy it in smaller portions.