Preheat your oven to 350°F (175°C).
Peel and chop the sweet potatoes into chunks. Place them in a large pot.
Fill the pot with water until it covers the sweet potatoes. Add a pinch of salt to the water.
Boil the sweet potatoes until they are fork-tender, about 15-20 minutes.
Drain the sweet potatoes and return them to the pot. Mash them until smooth and creamy using a potato masher or an electric mixer.
Add the butter, brown sugar, eggs, milk, vanilla extract, and salt to the mashed sweet potatoes. Mix everything until well combined, creating a silky-smooth sweet potato mixture.
Grease a 9x13-inch baking dish and spread the sweet potato mixture evenly in it.
Sprinkle the mini marshmallows over the top of the sweet potato mixture, ensuring even coverage.
Place the dish in the preheated oven and bake for about 25-30 minutes or until the marshmallows turn golden brown and toasted.
Remove from the oven, let it cool for a few minutes, and serve warm.