Preheat the oven: Preheat your oven to 350°F and lightly grease a 9x13-inch baking dish with butter or nonstick spray.
Prepare the peaches: Peel and slice the peaches into a large bowl. Toss them with granulated sugar, cornstarch and lemon juice until evenly coated and glossy.
Spread the filling: Pour the peach mixture into the prepared baking dish, spreading it into an even layer.
Mix dry topping ingredients: In a separate bowl, whisk together the oats, flour, brown sugar, cinnamon and salt until combined.
Cut in cold butter: Add the cold, cubed butter to the dry mixture. Use your fingertips or a pastry cutter to work it in until the mixture looks like coarse, buttery crumbs with some pea-sized pieces remaining.
Top the peaches: Scatter the oat crumble evenly over the peach filling, covering it completely but leaving it loose and textured.
Bake until golden: Bake for 35-40 minutes, until the topping turns deep golden brown and the peach juices bubble thickly at the edges of the dish.
Cool slightly: Remove the crisp from the oven and let it rest for 10-15 minutes so the juices can thicken before serving.
Serve warm: Spoon the peach crisp into bowls while still warm, topped with ice cream or whipped cream if you like.