Place egg whites in a large bowl. Let stand at room temperature for 30 minutes. Preheat oven to 300 degrees F. Line two very large baking sheets with parchment paper or foil; set aside.
For meringue: Add salt, vinegar, and peppermint extract to egg whites. Beat with an electric mixer on medium speed until soft peaks form (tips curl). Gradually add sugar, 1 tablespoon at a time, beating on high speed until stiff peaks form (tips stand straight) and sugar is nearly dissolved.
Transfer meringue to a decorating bag fitted with a 1/2-inch star tip. Pipe 1-inch kisses 1 inch apart onto the prepared baking sheets. Bake all of the meringue kisses at the same time on separate oven racks for 7 minutes. Turn off oven; let meringues dry in oven with door closed for 1 hour. Lift meringues off paper or foil. Transfer to wire racks; cool completely.
In a small saucepan, combine chocolate pieces and shortening. Cook and stir over low heat just until melted. Remove from heat. Spread crushed candy in a shallow dish. Dip bottoms of meringues in chocolate, then dip in crushed candies. Place on waxed paper and let stand until chocolate is set. Makes about 192 meringue kisses.
Tip: To crush the peppermint candies, place the unwrapped candies in a resealable plastic bag; seal bag. Using a meat mallet, pound lightly to crush the candies.