For the filling: Toss the stone fruits, lemon juice, brown sugar, granulated sugar, cornstarch, vinegar, cinnamon, and salt in a large bowl until well mixed. Transfer to a large cast-iron skillet.
For the topping: Whisk the flour, brown sugar, baking powder, baking soda, and salt in a medium bowl. Add the shortening and rub it in with your fingers until the mixture resembles coarse meal. Add the butter and cut it in with a pastry cutter or your fingers until incorporated with a few pea-size pieces remaining. Add the buttermilk and fold in until the dry ingredients are evenly moistened.
Drop heaping spoonfuls of the topping mixture onto the stone fruits, spacing them 1 inch apart. Sprinkle the topping with the sesame seeds.
Bake until the topping is golden brown and the filling is bubbling, about 45 minutes. Serve hot or warm with ice cream, if you'd like.