Preheat oven to 350°F (175°C). Lightly grease a 9x13-inch baking dish with butter or cooking spray. Place the dish on a rimmed baking sheet to catch any drips.
Bring a medium pot of water to a boil. Score an X on the bottom of each peach. Blanch for 30-60 seconds, then transfer to ice water for 2 minutes. Peel and slice into 1/2-inch wedges.
In a large bowl, combine peaches, blueberries, sugar, lemon juice, lemon zest, cornstarch, cinnamon, and vanilla. Gently toss until evenly coated.
Pour the fruit mixture into the prepared baking dish and spread into an even layer.
In a separate bowl, combine oats, flour, brown sugar, cinnamon, and salt. Cut in the cold butter using a pastry cutter or fork until the mixture resembles coarse crumbs.
Scatter the crumble topping evenly over the fruit filling. Do not press down; keep the topping loose for a crisp texture.
Bake for 40-45 minutes, until the topping is golden brown and the fruit is bubbling vigorously around the edges. Tent with foil if topping browns too quickly.
Remove from the oven and let rest for at least 15 minutes before serving. This allows the filling to set up slightly.