Preheat the oven to 375°F (190°C). Lightly grease a 9x13-inch baking dish with butter or nonstick spray.
Blanch peaches: cut a small X into the bottom of each, boil for 30-45 seconds, then transfer to ice water. Peel skins, remove pits, and slice into 1/2-inch wedges.
In a large bowl, whisk together granulated sugar, brown sugar, cornstarch, cinnamon, and salt. Add peaches, lemon juice, and vanilla, and toss until evenly coated.
Pour the peach filling into the prepared dish and spread into an even layer.
In a medium bowl, whisk together flour, brown sugar, granulated sugar, cinnamon, and salt. Cut in cold butter using a pastry cutter or fingertips until coarse, pea-sized clumps form.
Sprinkle the crumble topping evenly over the filling, leaving some larger clumps intact. Place the dish on a rimmed baking sheet.
Bake at 375°F (190°C) for 40-45 minutes, until the topping is deep golden brown and the filling is bubbling at the edges. Tent with foil if browning too quickly.
Remove from oven and let rest for 15-20 minutes before serving. Serve warm, on its own or with desired toppings.