Make the filling: In a bowl, toss the plums with the sugar and cornstarch and let stand for 10 minutes.
Meanwhile, make the dough: Preheat the oven to 375°. In a food processor, pulse the flour with the cornmeal, sugar, candied ginger, baking powder and salt. Add the butter and pulse until crumbly. Add the milk and pulse until moistened.
Spread the filling in a 9-by-13-inch baking dish. Scoop 15 mounds of dough over the filling. Bake in the center of the oven for 1 hour and 15 minutes, until the fruit is bubbling and the topping is golden and crisp. Let cool for 1 hour before serving.