Preheat oven to 350°F. Spray 8 x 8 baking pan lightly with non-stick cooking spray. Place butter in bottom of pan and place in the oven for 1 - 2 minutes for butter to melt. Remove form oven and tilt pan to spread melted butter evenly.
Add brown sugar to melted butter and carefully stir until all the sugar is moistened with butter. Spread in an even layer in bottom of pan then top with blueberries.
In the bowl of a stand mixer fitted with paddle attachment, beat the granulated sugar, brown sugar and butter until light and fluffy 3 - 4 minutes. Beat in vanilla extract. Add eggs and buttermilk and continue beating until combined.
In a large bowl, whisk together flour, cornmeal, baking powder, salt and baking soda. Add slowly to the egg mixture, beating only until just blended. Spoon batter over the top of blueberries, spreading into an even layer.
Bake for 45 to 55 minutes, until knife inserted in the center comes out clean. Cool in pan on wire rack for 10 minutes. Run a sharp knife around the edges of the pan and invert the cake onto a serving platter. Best served warm or at room-temperature.