Heat oven to 400 degrees. Grease or line a baking sheet or cast-iron pot with parchment paper; set aside.
In a large bowl, whisk together the flours, sugar, baking soda, cream of tartar, and salt. Using your fingertips, work two tablespoons of softened butter into the dry ingredients until texture resembles coarse crumbs.
Add buttermilk and stir with a fork just until dough begins to come together. Turn the dough out onto a flour-coated work surface and knead just until loose flour gets incorporated, about 12 to 14 turns; do not overknead.
Pat dough into a 6 inch diameter round about 2 inches high; place on prepared baking sheet or cast-iron pot. Using small sharp knife dipped into flour, cut 1/2-inch-deep cross into the top of the dough.
Bake until golden brown and a skewer inserted into center of loaf comes out clean or internal temperature reaches 180 degrees, 40 to 45 minutes. Remove from oven and brush with 1 tablespoon of melted butter; Cool on wire rack to room temperature, about 30 to 45 minutes.