Place cubed sweet potatoes in a large pot and cover with cold water by 2 inches. Add 1 teaspoon of salt to the water. Bring to a boil over high heat, then reduce to medium and simmer for 15-18 minutes until the sweet potatoes are fork-tender and fall apart easily. Drain thoroughly in a colander and let steam-dry for 3 minutes to evaporate excess moisture.

Preheat your oven to 350°F (175°C) and generously butter a 9×13-inch (23x33cm) baking dish. Transfer the drained sweet potatoes to a large mixing bowl. Add melted butter, brown sugar, beaten eggs, milk, vanilla extract, cinnamon, nutmeg, and salt. Using an electric mixer on medium speed, beat for 2-3 minutes until completely smooth and fluffy with no visible lumps.

Pour the sweet potato mixture into your prepared baking dish, using a spatula to spread it evenly into all corners. Gently tap the dish on the counter 2-3 times to release any air bubbles. Smooth the top surface. Bake uncovered for 25-30 minutes until the casserole is set around the edges and jiggles only slightly in the center when gently shaken.

Remove the casserole from the oven and let it rest for 10 minutes. Arrange mini marshmallows in an even layer across the entire surface, or place halved large marshmallows cut-side down in neat rows. Pack them closely together for maximum coverage. For extra richness, brush the marshmallows lightly with melted butter.

Switch your oven to the broil setting (high) and position the rack 6-8 inches from the heating element. Return the casserole to the oven and broil for 2-4 minutes, rotating the dish halfway through for even browning. Watch constantly—marshmallows should turn golden brown with some darker caramelized spots. Remove immediately when perfectly toasted. Let rest 5 minutes before serving.