Heat the oven to 400 degrees F and adjust a rack to the center position. Whisk the flours, baking soda, cream of tartar, salt and sugar in a large mixing bowl. Add the butter and work it into the flour until incorporated, with the mixture resembling coarse crumbs.
Make a well in the center and add the buttermilk. Work the liquid into the flour mixture using a fork until the dough comes together in large clumps.
Turn the dough onto a work surface and knead briefly (10 to 14 turns) until the loose flour is just moistened. The dough will still be scrappy and uneven. Do not be tempted to over-work the dough, or the bread will be tough.
Form the dough into a slightly flattened round about 6 to 7 inches in diameter and place in a cast iron skillet (an 8? skillet works nicely). Score a deep cross on top of the loaf and place in the heated oven. Bake until golden brown and a tester comes out clean when inserted into the center of the loaf, about 40 to 45 minutes.
Remove from oven and brush top with the tablespoon of melted butter. Cool for at least 30 minutes before slicing. Serve slightly warm or at room temperature. Bread will keep for a day or two if tightly wrapped.