Preheat your oven to 375°F (190°C). Lightly grease an 8x8 inch baking dish or a 9-inch pie plate.

Prepare the filling: In a large bowl, gently toss the sliced peaches with the granulated sugar, cornstarch, vanilla extract, and cinnamon until the peaches are evenly coated. Pour the mixture into the prepared baking dish.

Prepare the topping: In a separate medium bowl, whisk together the flour, rolled oats, brown sugar, and salt.

Cut in the butter: Using a pastry blender or your fingertips, cut the cold butter into the dry ingredients until the mixture resembles coarse crumbs. Some pea-sized pieces of butter are desirable.

Assemble and bake: Sprinkle the topping evenly over the peach filling. Place the dish on a baking sheet (to catch any potential drips) and bake for 40 to 45 minutes, or until the topping is golden brown and the peach filling is bubbly.

Cool slightly and serve: Let the crisp cool on a wire rack for at least 15 minutes before serving. Best served warm with vanilla ice cream or fresh whipped cream.