Beat egg whites until stiff. Add confectioner's sugar gradually. Gradually add granulated sugar. Fold in vanilla and pecan halves. Drop by rounded teaspoonfuls onto a greased cookie sheet. Place them about 2 inches apart. Bake in a very slow oven (300 degrees) for about 12-15 minutes or until firm and delicately browned at the edges. Cool completely. Store in an air tight container, or the humid salt air will soften them.