1. Preheat the oven to 400 degrees. Butter or line 2 rimmed baking sheets.

2. In a large bowl, whisk together the flour, baking powder, baking soda, and salt. In another large bowl, beat together the buttermilk, egg, and sugar.

3. Stir two thirds of the flour mixture into the buttermilk mixture. Gradually add the melted butter, incorporating it thoroughly into the mixture. Stir in the remaining flour mixture and the currants. The dough should be slightly stiff. Add a little more flour if needed.

4. Turn the dough out onto a clean, well-floured surface and gently knead for under a minute. (Overkneading the dough will make it tough.) Separate the dough into 3 equal parts. Shape each part into a thick 5-inch circle. With a sharp knife, cut the circles into quarters. Arrange the wedges on the prepared baking sheets, spacing them about an inch apart. Brush with some melted butter and generously sprinkle with sugar. Bake for 20 to 25 minutes, until lightly browned on top. Serve warm or at room temperature.