Prepare the berries: Preheat the oven to 375 degrees F. Grease a 12-inch cast-iron skillet with butter and set aside. In a mixing bowl, combine the berries, granulated sugar, flour, lemon zest and balsamic vinegar. Pour into the pan and smooth into an even layer.
Make the topping: In another mixing bowl, mix both sugars, the flour, oats, cinnamon and salt. Cut in the butter until you have a coarse crumb and the flour is fully hydrated. Sprinkle this mixture evenly and loosely over the top of the berries. Bake, uncovered, until golden brown, crisp and bubbling, 35 to 40 minutes. Remove from the oven and let sit at least 10 minutes before serving.