Preheat the oven to 350 degrees F (175 degrees C).
Combine blackberries, 1 tablespoon sugar, and cornstarch in a bowl; place into an oven-safe ramekin.
Combine flour, oats, 2 tablespoons sugar, butter, and allspice in a bowl until butter fully incorporated; place on top blackberry mixture.
Bake in the preheated oven until top golden, about 20 minutes.