Adjust oven rack to middle position and heat oven to 425°F.
Place flour, baking powder, sugar and salt in large bowl or work bowl of food processor fitted with steel blade. Whisk together or pulse six times.
If making by hand, use two knives, a pastry blender or your fingertips and quickly cut in butter until mixture resembles coarse meal, with a few slightly larger butter lumps. Stir in currants. If using food processor, remove cover and distribute butter evenly over dry ingredients. Cover and pulse 12 times, each pulse lasting 1 second. Add currants and pulse one more time. Transfer dough to large bowl.
Stir in heavy cream with a rubber spatula or fork until dough begins to form, about 30 seconds.
Transfer dough and all dry, floury bits to countertop and knead dough by hand just until it comes together into a rough, sticky ball, 5 to 10 seconds. Form scones by patting the dough onto a lightly floured work surface into a 3/4-inch thick circle, cutting pieces with a biscuit cutter, and pressing remaining scraps back into another piece and cutting until dough has been used up. You can also make a round and cut it into 8 wedges before baking it.
Place rounds or wedges on ungreased baking sheet and bake until scone tops are light brown, 12 to 15 minutes. Cool on wire rack for at least 10 minutes. Serve warm or at room temperature.