Preheat the oven to 350°F (175°C). Grease an 8x8 inch baking dish well with the 1 tablespoon (14g) of vegan butter so the cobbler does not stick.
In a medium mixing bowl, whisk together the flour, brown sugar, baking powder, and salt until everything is evenly combined.
Pour in the melted vegan butter, plant milk, and vanilla extract. Whisk just until you have a smooth batter with no dry streaks left. The batter should be pourable but not thin.
Pour the batter into the prepared baking dish and spread it into an even layer with a spoon or spatula.
Scatter the blackberries evenly over the top of the batter. Do not stir them in. As the cobbler bakes, the batter will rise up around the berries.
Bake for 40-45 minutes, or until the top is golden brown, the centre looks set, and the berries are bubbling around the edges. If you gently shake the pan, the middle should not look liquid.
Let the cobbler rest for 10-15 minutes before serving. This gives the filling time to settle slightly and makes it easier to scoop.
Serve warm, as is or with vegan vanilla ice cream.
