Preheat oven to 400 degrees Fahrenheit and adjust oven rack to top third of oven. Line with parchment or grease a large baking sheet.
In a large bowl, combine flours, sugar, baking soda, cream of tartar, and salt. Blend in 2 tablespoons of the butter with a dough blender, fork, or by hand.
Stir in the buttermilk with a fork just until the dough comes together. Knead on a lightly floured surface to form the dough into a round loaf, about 12 turns. Be careful not to overmix to avoid a tough dough.
Place the loaf on the prepared baking sheet and gently form into a 6 inch wide, 2 inch high circle. Cut 2 perpendicular lines about 1/2 inch deep on top of the loaf in the shape of an X.
Bake in preheated oven until top is golden and toothpick inserted in center comes out clean, 40-45 minutes. Melt remaining tablespoon butter and brush over the bread. Let cool to room temperature before serving, about 40 minutes.