Preheat the oven to 300°F. Butter a 10-inch cast-iron pan.
Prepare the topping: Whisk together the flour, sugars, cinnamon, salt, and oats in a large bowl. Drizzle in the melted butter and stir until pea-sized clumps form. Spread the topping out evenly on a baking sheet and bake, stirring every 5 minutes, for about 15 minutes, or until golden brown. Remove from the oven and set aside.
Increase the oven temperature to 350°F. For the filling, whisk together the sugars, cornstarch, water, and lemon juice in a large bowl. Toss the peaches in the mixture. Melt the butter in a large sauté pan and sauté the peaches for 15 minutes over medium-low heat to soften. Add the blueberries and continue to cook until the liquid has thickened and the peaches are cooked through. Transfer to the buttered cast-iron pan.
Top evenly with the topping and sprinkle evenly with the 1 teaspoon granulated sugar.
Set the cast-iron pan on a baking sheet and bake for 10 to 12 minutes, until warm and bubbly. Serve warm.