1. Soften the vanilla ice cream in the microwave at high power for 10 seconds. Transfer the softened ice cream to a medium bowl and flatten it with a rubber spatula. Spread the apple butter on top and fold the ice cream over the apple butter 2 or 3 times. Freeze the ice cream until it is firm, about 40 minutes.
2. Meanwhile, in a microwave-safe bowl, melt the chopped chocolate at high power in 10-second bursts. Whisk the heavy cream into the chocolate. Put the grated ginger in a fine strainer set over the chocolate ganache and press to extract as much of the ginger juice as possible. Whisk the ginger juice into the chocolate ganache.
3. Scoop the apple-butter ice cream into bowls, drizzle with the ginger-chocolate ganache and serve with gingersnaps.