Preheat oven to 400 degrees. With a fork prick potatoes and on a baking sheet bake in middle of oven 1 hour, or until tender. Leave oven on. When potatoes are just cool enough to handle, halve lengthwise and scoop flesh into a 3-quart saucepan, leaving 1/4-inch-thick shells.
With a potato masher mash potatoes in saucepan with 3 tablespoons butter. Stir in milk and salt and pepper to taste. Transfer shells to baking sheet and brush insides with remaining 2 tablespoons butter. Season shells with salt and pepper. Mashed potatoes and shells may be prepared up to this point 1 day ahead and chilled, covered. Reheat mashed potatoes before proceeding.
Bake potato shells in middle of oven until golden, about 20 minutes. While shells are baking, cut basil into thin strips and stir about three fourths into warm mashed potatoes. Spoon mashed potatoes into shells and bake until heated through, about 10 minutes. Serve each potato half topped with 1/2 tablespoon sour cream and some remaining basil.