Preheat the oven to 375°F.
In a medium bowl, combine the flour, oats, granulated sugar, salt, cinnamon, and melted butter. Stir until large crumbs form. Place the crumble mixture in the refrigerator while preparing the filling.
Add the sliced peaches to a 9x13-inch baking dish, large casserole dish, or deep pie dish.
Sprinkle in the brown sugar, flour, cornstarch, salt, cinnamon, vanilla bean paste, and lemon juice. Toss gently until the peaches are evenly coated.
Sprinkle the chilled crumble topping evenly over the peaches.
Bake for 40–50 minutes, or until the topping is golden brown and the peach filling is bubbling around the edges.
Allow the crumble to cool for 10–15 minutes before serving.
Serve warm with vanilla ice cream or whipped cream, if desired.