In a large bowl, cream the butter until light and fluffy. Gradually add confectioners' sugar, cream and vanilla; beat on medium speed for 3-4 minutes. Shape into 3/4-in. balls.
In a microwave or heavy saucepan, melt chocolate chips and shortening; stir until smooth. Dip balls in melted chocolate; roll in peanuts. Place on waxed paper-lined baking sheets; refrigerate until set. Store in an airtight container in the refrigerator.