Preheat oven to 400°F and lightly butter am 11x7 or 9x9 baking dish.
Chop basil leaves. In a large bowl, stir together with blackberries and honey. Pour into prepared baking dish in an even layer.
In a mixing bowl, combine flour, brown sugar, oats, almonds, and salt. Cut butter into chunks and use a pastry blender, knife, or your fingers to mix in the butter and form into clumpy pieces. (You can also use a food processor.)
Scatter the topping evenly over the blackberries. If you have extra topping, freeze it for a later use.
Place in the oven and bake for 25-30 minutes, until topping is browned and crisp, and juices are bubbly.
Let cool at least 10 minutes before serving to thicken juices.