Boil potatoes for 15-20 minutes or until potatoes are tender when pierced with a fork. Drain.
Mash slightly into big pieces, set aside.
In the bowl of a food processor or blender, puree the drained artichoke hearts with half the butter and milk.
Place the mixture in a bowl and add the still warm potatoes and remaining butter and milk and mix/mash until you get the desired consistency or until smooth.