Preheat your oven to 350°F (175°C). Lightly grease an 8x8 baking pan.
In a large bowl, gently stir together the blackberries, granulated sugar, lemon juice, lemon zest, and all-purpose flour. Transfer the mixture to the prepared baking pan.
In a medium bowl, combine the granulated sugar, all-purpose flour, baking powder, and salt for the topping. Add the vanilla extract and melted butter, stirring until fully combined. The mixture should resemble a crumbly dough.
Press pieces of the topping mixture together with your fingers to form flat, irregular-shaped pieces. Arrange the pieces of topping evenly over the blackberry filling.
Bake for 30-35 minutes, until the berries are bubbling and the topping is beginning to turn light golden brown.
Allow the cobbler to cool on a wire rack for about 15 minutes before serving. The juices will thicken as it cools.
Serve warm, with a scoop of vanilla ice cream on top.