In a large bowl, cream shortening and sugar until light and fluffy. Beat in the egg yolks, milk and vanilla. Combine the flour, salt and baking powder; gradually add to creamed mixture and mix well. Cover and refrigerate for 30 minutes.
Meanwhile, in a small bowl, beat the egg whites, salt, vinegar and vanilla until soft peaks form. Gradually add sugar; beat until stiff peaks form. Fold in chocolate chips. Transfer half of the meringue to another bowl. Fold peppermint candies into one portion and spearmint candies into the remaining portion.
Shape cookie dough into 1-in. balls. Place 2 in. apart on ungreased baking sheets. Flatten with a glass dipped in sugar. Drop meringue by teaspoonfuls into the center of each cookie. Bake at 325° for 18-20 minutes or until lightly browned.
Any extra meringue can be dropped by tablespoons onto baking sheets and baked as directed.