Preheat your oven to 350°F (175°C). To peel peaches easily, score an X on the bottom of each, blanch in boiling water for 30 seconds, then transfer to an ice bath. The skins will slip right off. Slice peaches into ½-inch wedges directly into a large mixing bowl.
Toss the sliced peaches with granulated sugar, lemon juice, vanilla extract, cornstarch, and cinnamon until evenly coated.
In a medium bowl, combine the oats, flour, brown sugar, cinnamon, and salt. Add the cold cubed butter and use your fingertips to work it into the dry ingredients until the mixture resembles coarse crumbs with pea-sized butter pieces remaining.
Transfer the peach mixture to a 9x9-inch baking dish, spreading it evenly. Sprinkle the oat topping uniformly over the peaches, covering them completely.
Bake in the preheated oven for 35-40 minutes, or until the topping is golden brown and the filling is bubbling around the edges. For optimal results, rotate the dish halfway through baking to ensure even browning.
Allow your peach crisp to cool for at least 15 minutes before serving. This cooling period allows the filling to set slightly, making it easier to portion while still maintaining that desirable warm quality.