Preheat oven to 375 degrees. Prepare 2 cookie sheets by covering with parchment paper.
In large bowl, cream together butter and peanut butter. Add sugars, mix well. Beat in eggs and vanilla extract. Mix in flour. Refrigerate for 15 minutes.
Roll dough into 1" balls, place about 2" apart on prepared cookie sheets. Using a fork- moistened and dipped in sugar- flatten each cookie and press criss cross pattern into top. Bake in preheated oven for 8-10 minutes. Allow to cool for 1 minute on cookie sheet, then remove from pan to finish cooling.
Place chocolate chips and shortening in small plastic or glass bowl, and melt in microwave. Dip each cookie in chocolate. I only coat 1/2 of the cookie, makes a pretty presentation! Allow chocolate to firm and serve or store in air-tight container.