In a one-quart wide-mouth jar, layer powdered sugar, then cocoa, packing each layer as tightly as possible. Wipe the inside of the jar with a paper towel to remove any excess cocoa before adding the next layer. Add nondairy creamer to jar, packing tightly. Add peppermint pieces. Fill any remaining space in top of jar with a layer of mini marshmallows; secure lid. Give with the following instructions: Empty jar into a large mixing bowl; blend well. Spoon mixture back into jar. To serve, add 3/4 cup boiling water to 1/4 cup cocoa mixture; stir to blend.