In a large pot of salted water, bring the fingerling potatoes to a boil and cook for 15 to 20 minutes until fork tender. Strain and let the potatoes cool until safe to handle.
Put the potatoes in a food processor. Add the vanilla sugar, 1/2 cup milk, and salt. Puree until creamy. Let the potatoes cool
Meanwhile, add the heavy cream and the remaining 1 cup milk to a heavy bottom saucepan. Split the vanilla bean and scrape the paste into the cream. Add the vanilla bean and bring to a slow steam, with bubbles forming just around the edges of the pan.
Whisk the egg yolks in a large bowl with the sugar until pale.
Drizzle in the steaming cream mixture, a little at a time, whisking constantly. Mix 3 cups of the pureed potatoes into the custard base.
Return the mixture to the heat and allow to thicken, about 7 to 10 minutes. You are looking for a consistency that coats the back of a spoon smoothly.
Remove from the heat and pour into a bowl over an ice bath. Whisk in the huckleberry vodka. Cover with plastic wrap, with the wrap directly on the surface of the custard. Chill for 4 to 6 hours.
When ready to churn, remove the vanilla bean from the ice cream base and churn the ice cream in your ice cream maker according to directions.
Spoon half the ice cream into a container and swirl 1/4 cup of the jam in. Spoon the rest of the ice cream in and swirl in the remaining huckleberry jam. Cover and freeze until set.
Allow the ice cream to sit out for 10 minutes before scooping and serving.