Place the potatoes in a large saucepan and add cold water to cover.
Bring to a boil over high heat.
Reduce the heat to medium and cook for 10 to 15 minutes, or until the potatoes are tender when tested with a sharp knife.
Drain and return to the pan.
Mash the potatoes well.
Warm the milk in a small saucepan over medium heat.
Gradually add to the potatoes and mix well.
Add the goat cheese, basil, pepper, and salt.