1. In the bowl of an electric mixer fitted with the paddle attachment, cream together butter and sugar. Beat until smooth. Add in egg and beat until well incorporated, scraping down the bowl, if necessary. Add in vanilla. Beat until smooth. With mixer on low, add in salt and flour. Mix until completely incorporated and dough is uniform. Shape dough into a cylinder with a diameter of about 2-3 inches. Wrap in parchment paper and freeze for at least 25 minutes.
2. Preheat oven to 350 degrees. Slice dough into 1/8 inch disks and place on baking sheets, about a half inch apart. Once you have made 30 cookies, wrap up the cookie dough, freeze, and save for another time. Bake for 8 minutes. Place on a cooling rack and let cool completely.
3. Mix together peanut butter and powdered sugar. Form into small disks and press onto cookies. Melt chocolate in a microwave safe bowl for 30 second intervals, and mix well after each interval. Coat cookies completely in chocolate and lift out with a fork. Place on a parchment lined baking sheet and let set, or freeze to speed up the process.