Preheat oven to 425°.
Lightly spoon flour into dry measuring cups; level with a knife. Combine flour, 3 tablespoons granulated sugar, baking powder, and salt in a bowl; stir with a whisk. Cut in butter with a pastry blender or 2 knives until mixture resembles coarse meal.
Combine 1/2 cup milk, vanilla, and egg white in a bowl. Add milk mixture to flour mixture, stirring just until moist (dough will be soft). Turn dough out onto a lightly floured surface. Sprinkle surface of dough with dried currants. With floured hands, knead 4 times or just until the currants are incorporated.
Pat dough into an 8-inch circle on a baking sheet lined with parchment paper. Cut dough into 12 wedges, cutting into, but not through, dough. Brush 2 teaspoons milk over surface of dough; sprinkle with 2 teaspoons turbinado sugar. Bake at 425° for 17 minutes or until golden. Serve warm, or cool on a wire rack.