Heat the oven to 400°F. Pierce the sweet potatoes, place on a lined baking sheet and roast for 50 to 60 minutes until completely soft. Split and scoop out the flesh; reduce the oven to 350°F.
Melt the 5 tablespoons butter in a small light-colored saucepan over medium heat. Cook for 3 to 5 minutes, swirling, until the milk solids turn golden brown; immediately pour into a heatproof bowl.
Mash the sweet potato flesh with browned butter, half-and-half, brown sugar, vanilla, salt and nutmeg. Let cool until warm rather than hot, then beat in the eggs.
Grease a 2-quart baking dish with the teaspoon butter and spread in the filling. Bake for 25 to 30 minutes until the center reaches 160°F.
Scatter marshmallows evenly over the hot filling and bake for 5 minutes more, watching closely, until puffed and golden. Rest for 10 minutes before serving.