Preheat oven to 350 degrees F (175 degrees C). Grease an 8-inch baking pan.
Mix blackberries, cinnamon, and lemon juice together in a bowl until coated. Pour into the prepared baking pan.
Combine 3/4 cup sugar, flour, and baking powder together in a separate bowl; stir in milk and butter. Spoon batter over blackberry mixture, covering as much as possible.
Stir remaining 3/4 cup sugar and cornstarch together in a bowl; stir in boiling water until sugar and cornstarch are dissolved. Pour mixture over berry mixture.
Bake in the preheated oven until a toothpick inserted in the center comes out clean, 45 to 50 minutes.
