In a large mixing bowl, whisk together the flour, cornstarch, baking powder, allspice, salt, and sugar.
Add the cold butter and rub it into the dry ingredients with your fingertips until the mixture resembles fine breadcrumbs.
Stir in the currants, dates, or chocolate chips.
Gently bring the dough together using your hands, adding a small splash of milk or water only if the mixture is too crumbly to hold.
Roll the dough out on a lightly floured surface to about 1/4 inch thick.
Use a 2 1/2 inch round cutter to cut out the cakes.
Heat a griddle or heavy skillet over medium-low heat. Cook the cakes in batches for 2–3 minutes on each side, until golden brown and cooked through.
While still warm, dust with sugar and enjoy.