Pierce the potatoes with a fork. Place on the top rack of the grill. Rotate after 45 minutes. Grill until tender, about 1 ½ hours.
Remove from the heat and set aside to cool. When cool to the touch, cut in half. Using a spoon, spoon the soft potato out of the skins. Discard the skins.
In a large saucepot, melt the butter. Use a potato ricer to mash the potatoes into the butter. Stir in half and half, chicken broth and seasonings and heat over low to medium heat, stirring until smooth.
To make on the Big Green Egg, use the platesetter.To make on a campfire, wrap the potatoes in foil and place into the hot coals.