Preheat your oven to 350°F (175°C). Lightly grease a 9x13-inch baking dish or a similar-sized oven-safe dish.

In a large mixing bowl, combine the sliced peaches, granulated sugar, cornstarch, vanilla extract, and 1/2 teaspoon of ground cinnamon. Stir gently to coat the peaches evenly, then transfer the mixture to the prepared baking dish.

In a separate bowl, prepare the topping by mixing the oats, flour, brown sugar, remaining 1/2 teaspoon of ground cinnamon, and salt. Stir until well combined.

Pour the melted butter over the oat mixture and stir until the mixture forms a crumbly texture.

Evenly sprinkle the cinnamon-oat topping over the peach mixture in the baking dish.

Bake in the preheated oven for 40-45 minutes, or until the topping is golden brown and the peach filling is bubbling around the edges.

Remove the peach crisp from the oven and allow it to cool for 10-15 minutes before serving.

Serve warm with a scoop of vanilla ice cream or a dollop of whipped cream, if desired.