Mix the flour, brown sugar, cinnamon and salt in a medium bowl.
Combine the butter into the mixture with your fingers until no longer floury and crumbs form. Freeze until ready to use.
On the grill, using a disposable foil pan or grill-proof pan, combine blueberries, strawberries, blackberries, raspberries, sugar, and cornstarch. Stir well and let cook until fruit starts to release its juices.
Cover fruit with crumble topping.
Cover pan with foil and cook at about 350-degrees for 20 minutes.