Put basil leaves in blender or processor with 2 T. of olive oil and blend. Cut tomatoes into big cubes, removing seeds, and lightly sauteé with remaining olive oil, a pinch of salt and a pinch of sugar.
Spread tomatoes evenly in a gratin dish and pour basil mixture over the tomatoes.
Cut butter into tiny pieces and let soften. Mix flour, breadcrumbs and parmesan together then mix in butter with fingertips until it resembles big grains of sand. Cover tomatoes with crumble and bake at 375 until top is golden brown, about 15 minutes.