In a medium bowl, whisk allspice, cinnamon, ginger, cloves, nutmeg, pepper, and salt. Add chocolate on top of spices.

In a small saucepan over low heat, heat cream until gently simmering but not boiling. Pour cream over chocolate and spices. Let sit 5 minutes, then whisk to incorporate until smooth. Pour into an 8"-by-8" baking pan and smooth into an even layer. Press plastic wrap on the surface of chocolate mixture and refrigerate until firm, about 1 hour.

Place crushed gingersnaps in a small bowl. Line a rimmed baking sheet with parchment.

Using a 1-tablespoon cookie scoop or measuring spoon, scoop 16 rounded tablespoons of chocolate mixture. Toss in gingersnap crumbs to coat. Roll between your palms to make balls, then roll in crumbs one more time. Transfer to prepared sheet.

Using the remaining chocolate mixture, scoop 8 more tablespoons, rolling between your palms to make uncoated balls. Place on prepared sheet. Freeze truffles until firm, at least 30 minutes.

In a small heatproof bowl, microwave white chocolate and oil in 20-second increments, stirring between each, until melted and smooth.

Working one at a time, drop one chilled uncoated ball into melted chocolate, spooning over to coat, and return to baking sheet. Sprinkle crushed gingersnaps on top. Repeat with 7 remaining uncoated balls.

Transfer remaining white chocolate to a piping bag fitted with a ¼"-diameter tip (or use a plastic bag with a corner cut off or a squeeze bottle). Drizzle over 8 of the crumb-coated balls.

Refrigerate truffles until firm, at least 30 minutes or up to overnight.

Make Ahead: Truffles can be made 1 week ahead. Store in an airtight container and refrigerate.