Heat the oven to 350°F and butter a 9-by-13-inch baking dish with 1 teaspoon of the melted butter.
Mash the drained sweet potatoes with the remaining butter, brown sugar, orange juice, cinnamon and salt until mostly smooth.
Stir in the beaten eggs until fully incorporated and spread the mixture evenly in the dish.
Bake uncovered for 25 to 30 minutes, until the center reaches 160°F and no longer looks wet.
Cover the surface with the miniature marshmallows and return the dish to the oven for 5 minutes, until they puff.
Broil for 30 to 60 seconds, watching continuously, until the marshmallow tops are spotted brown.
Rest for 10 minutes before serving.
