In a large mixing bowl, beat the peanut butter, softened butter, and vanilla until the mixture is smooth and creamy.
Gradually mix in the confectioners' sugar. The dough will become stiff as the sugar incorporates fully.
Using clean hands, shape the dough into small balls about 1 inch in diameter. Place them onto a wax paper-lined baking sheet.
Refrigerate the peanut butter balls for 30 to 60 minutes, or until they feel firm to the touch.
In the top of a double boiler, melt the chocolate chips and shortening over simmering water. Stir regularly to prevent scorching.
Insert a toothpick into each peanut butter ball, then dip it into the melted chocolate, leaving a small portion of the top uncovered to resemble a buckeye.
Place the dipped cookies back onto the baking sheet. Gently smooth over the toothpick hole with your finger.
Once all the cookies are dipped, refrigerate them until the chocolate hardens, about 30 minutes.