Grind the peanuts in a food processor until smooth. If the mixture seems too thick and grainy, add peanut oil a little bit at a time by drizzling a thin stream through the feed tube with the motor running. Puree until smooth and the consistency of peanut butter.
Transfer the peanut butter to the bowl of a mixer fitted with a paddle attachment (or any large bowl) and add the confectioners' sugar, graham cracker crumbs, and butter. Mix together until smooth. Form the mixture into bite-size balls and set aside on an un-greased cookie sheet. Chill until slightly firmed, about 30 minutes.
Meanwhile, arrange the paper cups on a cookie sheet. Melt the chocolate. Dip the tops of the peanut butter balls into the melted chocolate and set each one, chocolate side up, in a paper cup. Let the chocolate set before serving, about 30 minutes at room temperature (or refrigerate 10 minutes if you're in a hurry).
Store in an airtight container for up to 1 week.