Heat your oven to 375F. Grease a 9-inch cast iron skillet or another heavy baking pan with butter.
In the bowl of a standing mixer fitted with the paddle attachment, cream together the butter and the sugar until light and fluffy, about 3 minutes. Beat in the eggs one at a time, stopping to scrape down the sides of the bowl as needed. Beat in the cornmeal.
In a small bowl, stir together the flour, baking powder and soda, and salt. Mixing on low speed, add the dry ingredients in 3 additions, alternating with the milk/buttermilk, and starting and ending with the dry ingredients.
Scrape the batter into the greased pan, then arrange the halved figs on top. Bake until the cornbread is golden brown and a toothpick inserted into the center comes out clean, about 40-50 minutes.
Serve warm, with spoonfuls of ricotta, if desired. The cornbread keeps, tightly covered, for several days. Just lightly toast slices in a toaster oven before serving and you’re good to go.
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