Preheat the oven to 200° and position 2 racks in the middle. Line 2 large baking sheets with parchment paper.
In a large bowl, beat the egg whites at medium speed until frothy. Add the cream of tartar and beat at medium-high speed until very soft peaks form. Add the superfine sugar, 1 tablespoon at a time, beating for 10 seconds between additions. Add the lemon zest and the vanilla and almond extracts and beat until the meringue is stiff and glossy, about 1 minute longer. Sift the cornstarch and ginger over the meringue and fold in with a large spatula.
Spoon the meringue onto the prepared baking sheets in walnut-size mounds, lifting the spoon each time to form little peaks. Place 2 currants in each for eyes. Bake the meringues for 45 minutes. Turn the oven off and let them stand in the oven until completely cool, at least 3 hours or overnight. Gently lift each meringue off the paper and transfer to a plate to serve.
The meringues can be stored in an airtight container for 2 days.