Preheat oven to 325°F. Coat a baking sheet with cooking spray. Put a kettle of water on to heat for a water bath.
Spread gingerbread cubes on prepared baking sheet and bake until toasted, 25 to 30 minutes. Divide among six 6-ounce ( ¾-cup) ramekins. Sprinkle with chopped crystallized ginger.
Whisk eggs and sugar in a large bowl until blended. Whisk in milk and vanilla. Divide mixture among prepared ramekins and let stand for 10 minutes.
Place ramekins in a shallow roasting pan and pour in enough boiling water to come halfway up the sides of the ramekins. Bake until puddings are set, 40 to 50 minutes. Transfer to a wire rack to cool.
Before serving, dust puddings with confectioners' sugar and garnish with julienned crystallized ginger. Serve warm or chilled.