1. In a 9- to 10-inch (23-25cm) cast iron skillet, melt the 4 tablespoons of butter and the brown sugar together, stirring frequently, until the sugar is moistened and liquefied. When the mixture starts to bubble, remove from heat and set the pan aside.
2. Preheat the oven to 350ºF (180ºC).
3. In a small bowl, whisk together the flour, cornmeal or polenta, baking powder, and salt.
4. In the bowl of a stand mixer, or by hand in a mixing bowl with a spatula, beat the ½ cup of butter, granulated sugar and lemon zest at medium high speed for 3 to 5 minutes, until very light and fluffy.
5. Reduce the speed of the mixer to medium and add the eggs one at a time, stopping the mixer to scrape down the sides. Mix in the vanilla extract.
6. At low speed, add half of the flour mixture, then the milk, then the remaining dry ingredients, mixing just enough so that they’re all combined. Do not overmix.
7. Distribute the cranberries in the prepared pan over the brown sugar mixture and shake the pan so they are in a relatively even layer. Spoon the batter over the cranberries in four mounds, then use a spatula to spread the batter evenly over the fruit.
8. Bake the cake until the top is golden brown and a toothpick inserted into the center comes out clean, about 50 minutes. Remove from the oven, wait 10 minutes, then run a knife around the cake. Place a serving platter overturned on top of the cake in the skillet, then using oven mitts to cover your hands, flip the two over simultaneously, until the cake releases from the pan.