Halve and cut the peaches, then cut them into thin slices and place in a large bowl. Add the lemon juice, sugar, and cornstarch and toss well to combine. Gently fold in the blueberries.

Transfer the fruit mixture to a 10-inch skillet (cast iron is preferable) and set aside. In a food processor, combine the oats, brown sugar, cinnamon, and salt and pulse to combine and break down the oats somewhat. Add the butter and pulse until the pieces of butter are the size of peas.

Sprinkle the topping mixture evenly over the fruit. Cover and cook over medium heat until hot and bubbly, about 12 minutes. Turn off heat, remove the lid, and let stand for another 5 minutes to cool slightly. Serve warm or at room temperature.