Add the rinsed blackberries to the slow cooker. Sprinkle over the 1/4 cup sugar, 1 Tablespoon cornstarch and 2 Tablespoons melted butter. Stir these items together. If you don't want whole berries in your cobbler and want a pureed sauce, take a potato masher and squish the berries at this step.
In a medium-sized bowl, add the dry ingredients listed in the cobbler layer above (flour, sugar, baking powder and salt) stir. Then add the wet ingredients (vanilla, milk and melted butter). Stir until combined, some lumps are fine, do not over mix.
Evenly pour this batter over the blackberries. Spread out with a spatula if needed.
In a small ramekin or bowl add the Tablespoon of sugar and 1/4 tsp. cinnamon, mix. Sprinkle this over the batter.
Place the lid on the slow cooker. Cook on HIGH for 2 hours and 30 minutes. Do not open the lid during the cooking time. If your center is still jiggly you will want to place the lid back on and cook for a bit longer.
Switch the slow cooker to the warm setting to serve. Serve with ice cream or whipped cream.