Preheat the oven to 425 degrees F.
Butter and flour an 8-inch round deep cake pan or panettone mold. In a mixer, cream the butter with the eggs and egg yolks until pale yellow, 3 to 4 minutes.
Replace the beater with the dough hook attachment, and with the mixer running, add half of the flour. Add half the milk and mix for 1 minute. Add the remaining flour followed by the remaining milk and all of the sugar and mix well. Continue mixing and kneading with the dough hook until the dough becomes dry enough to handle. Turn the dough out onto a floured surface and sprinkle with the currants, orange zest, cream of tartar, and baking soda. Knead by hand for 5 to 10 minutes.
Place the dough in the prepared pan and bake for 35 to 45 minutes, or until a wooden skewer inserted in the center comes out clean. The top will be quite cracked. Remove from the oven, invert onto a rack and cool. Slice into wedges to serve.