Preheat the oven to 400 degrees F (200 degrees C).
Toss blackberries with 1 ¼ cups sugar and 1 ½ tablespoons flour in a mixing bowl. Spread into a 9x9-inch baking dish, and dot with 1 ½ tablespoons of butter.
Whisk 1 1/2 cups flour, baking powder, salt, and 2 tablespoons sugar together in a separate bowl. Cut in softened butter until mixture resembles bread crumbs. Stir in milk and egg until combined. Drop batter over the berries by the spoonful.
Bake in the preheated oven until the fruit is tender and the topping is golden brown, 20 to 30 minutes.