Preheat the oven to 350 degrees F. Butter a shallow 2 1/2-quart baking dish.
Prepare the filling: Toss the peaches and plums in a medium bowl with the brown sugar, honey, ginger and salt. Sprinkle in the flour and toss to coat. Pour into the prepared baking dish.
Make the biscuits: Whisk the flour, granulated sugar, baking powder and salt in a medium bowl. Cut in the butter with your fingers or a pastry blender until the mixture looks like coarse meal with pea-size bits of butter. Add the buttermilk and stir with a fork until a shaggy dough forms. Turn the dough out onto a lightly floured surface and knead a few times to bring it together. Pat into an even 1/4-inch thickness. Cut out the biscuits with a 2-inch-round cookie cutter, rerolling the scraps as needed.
Arrange the biscuits on top of the filling. Brush with buttermilk and sprinkle with coarse sugar. Bake until the biscuits are golden and the filling is bubbling, about 50 minutes.