Heat the oven to 425°F. Grease a 9-inch cast-iron skillet with 1 tablespoon of the butter. In a large bowl, mix together the cornmeal, cardamom, salt, sugar, and baking soda. In a separate bowl, mix the eggs and buttermilk together. Pour the buttermilk and the eggs into the large bowl with the dry ingredients and mix well. Add the remaining melted butter and whisk. Pour the batter into the skillet and bake for 15 to 20 minutes. Serve warm.