Preheat grill to 350° to 400° (medium-high) heat. Grill peppers, without grill lid, 5 minutes on each side or until peppers look blistered.
Place peppers in a large zip-top plastic freezer bag; seal and let stand 10 minutes to loosen skins. Carefully peel peppers. Cut each pepper lengthwise down 1 side, being careful not to cut through other side. Remove and discard seeds and membranes.
Cut potatoes into 2-inch pieces. Bring potatoes, salt, and water to cover to a boil in a large Dutch oven over medium-high heat, and cook 20 minutes or until tender; drain. Return potatoes to Dutch oven, reduce heat to low, and cook, stirring occasionally, 3 to 5 minutes or until dry.
Mash potatoes with a potato masher. Stir in buttermilk, butter, chiles, and half of goat cheese until blended. Spoon mixture into a gallon-size zip-top plastic freezer bag. (Do not seal.) Snip 1 corner of bag, and pipe mixture into each pepper; top with remaining goat cheese.
Grill peppers, covered with grill lid, over 350° to 400° (medium-high) heat 10 to 12 minutes or until cheese is melted.