Preheat the oven to 400F, and line a baking sheet with parchment paper.
Whisk together the flours, sugar, salt, baking soda and cream of tartar until well blended.
Cut the butter in, using a pastry cutter (or 2 knives) until it resembles very coarse breadcrumbs.
Pour in the buttermilk and stir very briefly, until it JUST comes together (it will be shaggy, see below).
Dump the mixture out onto a floured surface, and pat it into a round shape.
Using a serrated knife, cut a cross into the top (see photo).
Bake for 40 minutes, until the bread is golden brown.
Remove from the oven and brush with melted butter.
Allow to cool before cutting into slices or wedges.