Preheat the oven to 400 degrees F.
Wash and dry potatoes. Bake in the oven for 35 to 45 minutes, or until tender and not mushy. Remove from the oven and let cool.
Cut the potatoes in half. Scoop out the flesh of the potatoes and reserve for another use. Season with salt and freshly ground black pepper, and drizzle with melted butter.
Place the skins on a baking sheet and return to the oven to bake for about 10 minutes, or until crisp.
Top each skin with 1 ounce of brie and 1/4 cup walnuts. Place the skins on a baking sheet and broil until the cheese is bubbly; about 5 minutes. Garnish with chopped chives.