Preheat the oven to 350°F (175°C).
Prepare a 9-inch round cake pan by greasing it with butter and sprinkling brown sugar evenly across the bottom.
Arrange the blackberries over the brown sugar in the pan.
In a mixing bowl, whisk together the cornmeal, flour, baking powder, baking soda, and salt.
In another bowl, cream together the softened butter and granulated sugar until light and fluffy.
Add the eggs one at a time, mixing well after each addition, followed by the vanilla extract.
Gradually add the dry ingredients to the wet mixture, mixing just until combined.
Pour the batter over the blackberries and spread gently to even it out.
Bake in the preheated oven for 35-40 minutes or until a toothpick inserted into the center comes out clean.
Allow the cake to cool in the pan for about 10 minutes before inverting onto a serving plate.
Serve the cake warm or at room temperature, garnished with additional blackberries or whipped cream if desired.