In a large bowl, gently mix together blackberries, strawberries, sugar and flour. Pour the filling into a 9-inch ceramic or glass pie dish.
The Topping:
In a large bowl, stir together flour, brown sugar, oats, gingersnap crumbs, salt and cinnamon.
Add butter and, using your fingers, work the butter into the flour mixture to form a coarse meal. Sprinkle the topping over the berries.
Bake until the berries are bubbling thickly and the top is golden brown, 40 to 45 minutes. Check halfway through cooking and cover with foil if the top is turning too dark.
Remove from oven and let cool for 15 minutes before serving. Serve with vanilla ice cream.