Place oven rack in the center of oven, and preheat to 375F.
In a large bowl, stir together the brown sugar, 1 1/2 tablespoons of flour, 1/2 teaspoon cinnamon, the ginger, and the crystallized ginger. Add the plums, and stir to coat. Place the plums cut-side-down in a deep, 9-inch pie plate.
In a medium bowl, whisk together the sugar, remaining 1 cup of flour, the remaining 1/2 teaspoon cinnamon, the baking powder, and salt. Add the egg, then use your hands to thoroughly combine, squeezing and pinching to make a crumbly topping. Sprinkle it in an even layer over the plums. Drizzle with the melted butter, and bake 30-35 minutes, until the crumble is browned and the plums are very tender. Let sit on a wire rack to cool.
Serve warm or at room temperature.