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.
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.
Scoop the apple-butter ice cream into bowls, drizzle with the ginger-chocolate ganache and serve with gingersnaps.