Preheat the oven to 350°F and spray an 8 by 8-inch baking pan with nonstick cooking spray or grease with butter.
Make the filling and stir together the blackberries, sugar, flour, and lemon juice. Transfer the filling to the prepared baking pan and spread evenly.
Next, make the biscuit topping. Stir together the flour, sugar, and salt. Stir in the melted butter and vanilla. Gradually stir in the milk until a thick, scoopable batter forms. Add scoops of the batter over the berry filling to cover it.
To finish, cut the cold butter into small cubes and scatter over the biscuit topping. Stir together the sugar and cinnamon and sprinkle over the biscuit topping.
Bake for about 45 minutes, until the topping begins to brown and the filling is bubbling. Remove from the oven and serve warm or at room temperature.