Add chocolate chips to a large bowl. Set aside.
Add milk, sugar and butter in a pan and heat at medium heat until butter is melted and ingredients are combined.
Turn heat to medium high until mixture is bubbling, then turn down to medium low.
Stir continually and keep on heat for 7 minutes.
Pour mixture over dark chocolate chips and stir until all the chocolate is melted.
When it is a little cooled, add in marshmallows. They should not be melting.
Add fudge to a greased pan, top with peppermint, then let set for several hours before serving. You can also let it set in the refrigerator.