Preheat the oven to 375ºF. To make the topping, melt the butter in a 10- to 11-inch cast-iron skillet over medium heat. Add the maple syrup and swirl around for a minute or two, just until it starts to turn brown (not black) and remove from the heat. Allow to cool slightly and add the berries.
To make the cake, combine the cornmeal, flour, baking powder, and salt in a bowl and stir until blended. In an electric mixer, cream the butter with the maple syrup until creamy, about 3 minutes on medium speed. Add the eggs, one at a time. On low speed, add the flour mixture alternating with the yogurt (or sour cream) in three batches, ending with the flour. Scrape the batter into the skillet.
Bake for 75 minutes, or until a knife point inserted near the center comes out clean. Remove from the oven and let cool for 15 minutes. Run a knife around the edges of the pan, invert onto a plate, and serve.