1. Preheat oven to 400 degree F. Cut 6 squares of foil large enough to wrap each potato. Pierce potatoes on all sides with a fork and place each on a piece of foil. Drizzle potatoes evenly with oil, sprinkle with the coarse salt and wrap in foil. Place on rack in middle of oven and bake until very tender, about 1 hour.
2. Heat milk with butter over moderate heat in a small saucepan just until hot (do not boil). Carefully remove potatoes from foil and let cool slightly, about 10 minutes. Halve potatoes lengthwise and scoop out into a bowl, reserving skins of 8 halves with a 1/4-inch border of potato around skin. Mash potatoes with milk mixture until almost smooth. Stir in sour cream, chopped chives, and 1/4 cup cheese; salt and pepper to taste. Mound mixture into reserved potato skins and sprinkle with remaining 1/4 cup cheese.
3. Bake in upper third of oven until golden brown, about 30 minutes. Garnish with snipped chives. Makes 8 servings.