In a large mixing bowl, combine sliced plums, granulated sugar, light brown sugar, cornstarch, and cinnamon.
Preheat the oven to 375°F. Spoon the plum mixture into a 9- or 10-inch baking dish.
In a medium mixing bowl, combine flour, granulated sugar, baking powder, and salt.
Add the cold cubed butter to the flour mixture. Using a pastry blender or two forks, cut in the butter until the mixture resembles coarse crumbs. Stir in the milk just until the dough comes together.
Crumble the dough over the plum mixture in the baking dish.
Bake in the preheated oven for about 45 minutes, or until the topping is golden brown and the filling is bubbly.
Allow to cool slightly before serving. Serve with a scoop of vanilla ice cream on the side.