In a large bowl, mix butter with powdered sugar and vanilla extract until it is fully combined. Fold in the M&Ms and chocolate chips. Roll the mixture into balls and place onto a large plate.
Freeze for at least 20 minutes. Place the chocolate chips into a microwave-safe bowl, and heat in the microwave in 30-second intervals, stirring well until it is fully melted and smooth.
Fully coat each truffle in the melted chocolate and set onto a plate. Let sit until it is completely set.