Heat the oven to 350 degrees F. Use 1 tablespoon of the butter to grease a 2 quart flameproof baking dish.
Peel the sweet potatoes and slice them 1/8-inch thick. Place 1/3 of the potatoes in the bottom of the baking dish. Season with salt and sprinkle over 1/3 of the pecans. Repeat 2 more times. Pour the coffee liqueur and cream over the potatoes. Spread the brown sugar evenly over the top and dot with the remaining butter. Cover the dish with aluminum foil and bake until the sweet potatoes are tender when poked with a sharp knife, about 50 to 60 minutes. Remove the dish from the oven and turn on the broiler. Remove the foil and cover the sweet potatoes evenly with the marshmallows. Put the dish under the broiler until the marshmallows are lightly browned, about 1 minute. Let cool a bit before serving.