Preheat your oven to 375°F and butter a 9x13-inch baking dish.
Toss the sliced plums with 1/2 cup sugar, cornstarch, and vanilla extract, then spread them evenly in the prepared baking dish and let sit for 10 minutes.
In a large bowl, whisk together the flour, remaining 1/4 cup sugar, baking powder, and salt, then cut in the cold butter using a pastry cutter or fork until the mixture resembles coarse crumbs.
Stir in the milk until just combined, then drop spoonfuls of the dough over the plum mixture.
Sprinkle the coarse sugar over the top and bake for 40-45 minutes until the topping is golden brown and the fruit is bubbling.
Allow to cool for at least 15 minutes before serving warm with ice cream or whipped cream.