Preheat the oven to 350 degrees F.

Set a 10-inch cast iron skillet over medium heat and add the butter. Once the butter has melted, add the cranberries, 1 cup of the sugar, 2 teaspoons of the lemon zest and the lemon juice. Stir and cook until the cranberries wilt and have released most of their juice, about 5 minutes. Use a slotted spoon to remove the cranberries from the pan and set aside as you continue to cook the cranberry juices, if desired. The juices should bubble and thicken as it cooks. Continue to cook for 2 minutes, then return the cranberries to the pan, if removed, and, using a spoon, arrange the berries so that they cover the bottom of the pan in 1 even layer, patting them down to be sure. Remove the skillet from the heat and allow to cool for 20 to 30 minutes.

While the skillet cools, prepare the cake batter. In a medium bowl, sift together the flour, baking powder and salt. Stir in the cornmeal.

In a large bowl using an electric mixer, beat the eggs, egg yolk, milk, olive oil and the remaining 2 teaspoons of lemon zest until frothy. Add the remaining 3/4 cup of sugar and mix to combine. Pour the wet ingredients over the dry ingredients and mix just until the batter is smooth. Pour the batter into the cooled skillet over the cranberries and place in the oven to bake until a toothpick inserted into the center of the cake comes out smooth, about 30 minutes.

Remove the skillet from the oven and allow to cool on a wire rack for 20 minutes. Place a plate over the top of the skillet and, working quickly, invert the plate and the skillet and give the skillet a quick tap on a solid work surface to help dislodge the cake from the pan onto the plate. Allow to cool to warm before serving. Cake may be served either warm or at room temperature.