Preheat oven to 350°. Combine sugar and cocoa, stirring well. Beat egg whites and cream of tartar at high speed of an electric mixer until foamy. Gradually add sugar mixture, 1 tablespoon at a time, beating until stiff peaks form and sugar dissolves (2 to 4 minutes). Stir in vanilla and chocolate mini-morsels.
Drop by teaspoonfuls onto cookie sheets lined with aluminum foil. Place in oven, and immediately turn oven off. Do not open door for at least 8 hours. Remove from oven, and carefully peel cookies from foil.