Cook the sweet potatoes: Boil the peeled and cubed sweet potatoes in a large pot of water until fork-tender, about 15-20 minutes. Drain and set aside.
Preheat the oven: Set the oven to 350°F (175°C) and grease a 9x13-inch baking dish.
Prepare the sweet potato mixture: Mash the sweet potatoes in a large bowl. Add melted butter, brown sugar, eggs, vanilla extract, cinnamon, nutmeg, and salt. Mix until smooth.
Make the topping: In a separate bowl, combine pecans, brown sugar, flour, and melted butter. Stir until crumbly.
Assemble the casserole: Spread the sweet potato mixture evenly into the prepared dish. Sprinkle the pecan mixture over the top.
Add marshmallows: Scatter mini marshmallows over the pecan topping.
Bake: Place the casserole in the oven and bake for 25-30 minutes, or until the marshmallows are golden and the filling is bubbly.