Preheat oven to 375°F (190°C).
Grease a 9x13-inch baking dish lightly with butter or nonstick spray.
In a large bowl, combine peaches, granulated sugar, lemon juice, cornstarch, vanilla, and cinnamon.
Toss gently until peaches are coated evenly.
Pour peach mixture into prepared baking dish and spread evenly.
In another bowl, combine flour, oats, brown sugar, salt, and cinnamon.
Stir until well blended.
Add cold butter cubes to the bowl.
Cut butter into dry mixture with a pastry cutter, fork, or fingers until coarse crumbs form.
Sprinkle crumble topping evenly over peach filling, covering the surface completely.
Bake for 40–45 minutes until peach juices are bubbling and topping is golden brown.
Remove from oven and let cool for at least 15 minutes to allow filling to thicken.
Serve warm as is or with vanilla ice cream, whipped cream, or caramel drizzle.