For the filling: Whisk together the cornstarch and 1/4 cup water in the insert of a 6-quart slow cooker. Add the plums, granulated sugar and salt, and stir to combine.
For the topping: Whisk together the flour, granulated sugar, baking powder and salt in a large bowl. Add the butter and rub the mixture together with your fingers to form a coarse meal with some pea-size lumps. Add the half-and-half, and stir with a wooden spoon to form a wet dough.
Drop small spoonfuls of the dough over the plum mixture. Cover the slow cooker with a lid, and cook on high heat until the cobbler is bubbly and the biscuits are cooked through, 3 to 4 hours.
Rest the cobbler for 20 minutes. Spoon the cobbler into serving bowls, and then sprinkle with confectioners' sugar and top with a scoop of vanilla ice cream to serve.
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