Let egg whites stand in a large mixing bowl for 30 minutes. Cover a baking sheet with clean plain brown paper or foil; draw eight 3-inch circles. Add vanilla and cream of tartar to egg whites. Beat with an electric mixer on medium speed until soft peaks form (tips curl). Add sugar, a tablespoon at a time, beating on high speed until very stiff peaks form (tips stand straight) and sugar is almost dissolved. Fold in grated white chocolate baking square.
Spread or pipe meringue over circles on paper and shape into shells. Bake in a 300 degree F. oven for 30 minutes. Turn oven off; let meringues dry in oven with door closed for at least 1 hour (do not open door). Peel off paper. Store in an airtight container up to 1 week. Makes 8.