Preheat oven to 375°F (190°C) and grease a 9-inch square baking dish with butter.
In a large mixing bowl, combine sliced peaches, granulated sugar, lemon juice, cornstarch, and 1/2 teaspoon cinnamon.
Transfer peach mixture to the prepared baking dish and spread evenly.
In a separate medium bowl, whisk together oats, flour, brown sugar, 1/2 teaspoon cinnamon, and salt.
Incorporate cold cubed butter into the oat mixture using a pastry blender or fingertips until it forms pea-sized clumps.
Evenly distribute the crumble topping over the peach layer.
Bake for 40 to 45 minutes until the topping is golden brown and the peach juices are bubbling around the edges.
Remove from oven and let rest for at least 10 minutes to allow the fruit filling to set before serving.