Preheat the oven to 375 degrees F (190 degrees C). Grease a 9-inch baking dish with butter.

Add blackberries to the prepared baking dish.

Stir milk and eggs together in a bowl. Whisk in flour, sugar, and salt and mix until batter is smooth. Pour batter over blackberries.

Bake in the preheated oven on the middle rack until eggs start to set, about 25 minutes. Sprinkle brown sugar on top and bake until golden brown, about 20 more minutes.