In a separate bowl, mix together the flour, brown sugar, oats, cinnamon, and ginger. Rub the butter into the mixture until incorporated evenly and the mixture resembles little pebbles.
Spread the topping evenly over the filling. Cover with foil and bake for 45 minutes (if you don't cover them it will take a little longer to bake), until the filling is beginning to send up thick bubbles. Remove the foil and continue baking until the top is golden brown and crispy, about 15 minutes longer.
Serve hot or cold with vanilla ice cream, if desired.