Cream the butter and sugar smoothly; beat in the eggs and vanilla. Sift the flour, cornstarch and cream of tartar; add gradually, beating into the butter mixture. Put spoonsful of the dough about 2 inches apart on a buttered baking pan or cookie sheet. Bake in a moderately hot oven (400°F.) about 8 minutes, until the cookies have a golden brown edge.
When removing them from the pan they are soft; they become crisp when cool and are rich and delicious.