Preheat your oven to 350°F (175°C). Grease a 9x13-inch baking dish lightly with butter or nonstick spray.

In a large mixing bowl, combine the sliced peaches, granulated sugar, cornstarch, vanilla extract, and ground cinnamon. Toss until the peaches are evenly coated. Transfer the mixture to the prepared baking dish and spread evenly.

In another mixing bowl, prepare the topping by combining the rolled oats, flour, brown sugar, ground cinnamon, and salt. Stir to mix well.

Pour the melted butter into the oat mixture and stir until the ingredients are fully combined and crumbly.

Sprinkle the cinnamon-oat topping evenly over the peach mixture in the baking dish.

Bake the peach crisp in the preheated oven for 40-45 minutes, or until the topping is golden brown and the peaches are bubbling.

Remove from the oven and let cool for 10 minutes before serving. Serve warm, optionally with a scoop of vanilla ice cream or whipped cream.