Mix peanut butter, softened butter, and vanilla in a large bowl until smooth and combined.
Gradually mix in powdered sugar to form a thick dough firm enough to roll, using hands at end if needed.
Roll into 1-inch balls on a parchment-lined sheet; insert toothpicks and freeze 30 minutes.
Microwave chocolate and shortening in a microwave-safe bowl at 30-second intervals, stirring between each, until smooth.
Hold balls by toothpicks and dip in chocolate, leaving a small peanut butter circle exposed for the buckeye look.
Return to parchment; smooth toothpick holes with a finger. Refrigerate about 30 minutes until chocolate sets; store airtight in refrigerator.