1. Preheat oven to 375 degrees, with racks in upper and lower thirds. Stir together plums, berries, 1/3 cup granulated sugar, cornstarch, brown sugar, lemon juice, ginger, and pinch of salt in a large bowl. Transfer to a 2-quart baking dish.

2. Whisk together flour, baking powder, and remaining 1/2 teaspoon salt and 1/3 cup granulated sugar in a medium bowl. Cut butter into flour mixture using a pastry blender or two knives until only pea-size clumps remain.

3. Stir vanilla seeds into the cream to combine; add to flour mixture and stir with a fork just until a soft, sticky dough forms. Use a bench scraper or knife to divide dough into 10 equal pieces; arrange on top of filling. Brush dough with cream and sprinkle evenly with sanding sugar.

4. Place a parchment-lined baking sheet on lower rack of oven to catch juices. Bake cobbler on top rack until topping is golden brown and juices are bubbling, 55 to 70 minutes. If topping is browning too quickly, tent with foil. Let cool on a wire rack 1 hour before serving.