Whisk together the flour, sugar, baking soda, cream of tartar and salt in a large mixing bowl.
Stir in the buttermilk and 3 tablespoons of the melted butter, using a fork, then stir in the currants. Once combined, the dough should come together. Turn the dough out onto a floured surface. Knead gently for just a few turns until the dough can be shaped into a 6-inch round (do not over-knead).
Place the shaped dough into a cast-iron skillet or sheet tray. Cut an "x" into the top of the round loaf, using a knife.
Bake until the center has cooked through (testing with a skewer), about 40 minutes. Slather with the remaining tablespoon melted butter.