Preheat oven to 350 degrees.

In a large bowl, whisk together the cornmeal, flour, sugar, baking powder, baking soda and salt. Set aside.

In a small bowl, melt 4 tablespoons of butter. Whisk in the eggs and buttermilk. Pour the buttermilk mixture into the flour mixture and stir to combine thoroughly. Set aside.

In a 10-inch cast iron skillet, heat the remaining butter and olive oil over med-high heat until the butter is melted. Sprinkle the sugar over the butter and cook for 1 minute. Arrange the tomato slices in the bottom of the skillet and cook for 30 seconds. Pour the batter into the skillet and spread with a spatula so the bottom is covered. Transfer the skillet to the oven and bake for 30-35 minutes or until a cake tester inserted into the middle comes out clean. Remove from the oven and allow to cool for 10 minutes. Cover the skillet with a plate and turn the skillet over to remove the cornbread. Serve immediately or at room temperature. Best if enjoyed the same day.