In a 1- to 2-quart pan over high heat, bring cream to a boil. Meanwhile, place chopped chocolate in a bowl.
Pour cream over chocolate and stir gently with a flexible spatula until chocolate is melted and mixture is smooth. (If chocolate does not melt completely, place bowl over a pan of barely simmering water and stir until melted and smooth.) Stir in rum and candied ginger. Chill mixture until firm, at least 3 hours; if desired, cover and chill up to 1 week.
Line a 12- by 15-inch baking sheet with a piece of waxed paper. With a spoon, scoop out 1-tablespoon portions of chocolate mixture; place on waxed paper. If mixture is too firm to scoop, let stand at room temperature about 10 minutes.
Place 1/4 cup cocoa on a rimmed plate. Dust hands lightly with cocoa. With your hands, roll each scoop of chocolate mixture into a ball, then roll in cocoa to coat.
Place each truffle in a small paper candy cup (see notes). To store, place truffles between layers of waxed paper in an airtight container and chill. Advise recipient to chill as well, then bring to room temperature just before serving.
