Preheat the oven to 450°. Put the butter in a 10-inch cast-iron skillet and melt the butter in the oven.
Meanwhile, in a large bowl, mix the cornmeal with the cream of tartar, salt and baking soda. Add the buttermilk and eggs and stir to blend.
Remove the skillet from the oven and swirl to coat with the butter. Pour the melted butter into the batter and stir just until incorporated. Scrape the batter into the hot skillet and bake for about 35 minutes, or until crusty around the edge and springy to the touch. Invert the corn bread onto a rack and let cool completely.
The corn bread can be stored in the refrigerator for up 2 days.