Preheat the oven: Preheat your oven to 350°F (175°C) and butter a 9x9-inch baking dish or cast iron skillet.
Make the fruit filling: In a large bowl, toss peaches and blueberries with sugar, flour, lemon juice, cinnamon, nutmeg, and salt. Stir until evenly coated and pour into the prepared dish.
Make the topping: In another bowl, combine oats, flour, brown sugar, cinnamon, and salt. Add cold butter and cut it in using your fingers or a pastry cutter until the mixture resembles coarse crumbs.
Assemble and bake: Sprinkle the topping evenly over the fruit filling. Bake for 40–45 minutes, until the top is golden and the fruit is bubbling around the edges.
Cool and serve: Let it cool for 15 minutes before serving. Enjoy warm with ice cream or chilled the next morning.