Prepare the oven and pan. Preheat the oven to 400°F (200°C). Lightly grease a 9-inch square baking dish.
Mix the peach filling. Toss the sliced peaches with granulated sugar, 2 tablespoons of flour, cornstarch, 1 teaspoon cinnamon, and salt until evenly coated.
Fill the baking dish. Spread the peach mixture evenly in the prepared dish.
Make the crumble. Combine the brown sugar, remaining 1/2 cup flour, softened butter, and remaining cinnamon. Mix until moist crumbs begin to form.
Add the oats. Work the rolled oats into the butter mixture until you have a rustic, chunky crumble.
Top the peaches. Scatter the oat mixture evenly over the fruit without pressing it down too firmly.
Bake. Bake for approximately 20 to 25 minutes, or until the fruit is bubbling and the topping is lightly golden around the edges.
Rest before serving. Allow the peach crisp to stand for about 10 minutes so the hot fruit juices can settle and thicken slightly. Serve warm.