Preheat oven to 350°. Place potatoes in a large pot and cover with water. Bring to a boil, then reduce heat to medium-low and simmer until potatoes are fork-tender, about 15 minutes. Drain and let cool slightly.

Transfer potatoes to a large bowl. Add eggs, butter, milk, brown sugar, vanilla, and salt. Using a potato masher or fork, mash potatoes until combined. Transfer to a 13" x 9" baking dish.

In a medium bowl, mix brown sugar, flour, and butter until clumps form. Stir in pecans, then spread over potatoes. Top with marshmallows.

Bake casserole until cooked through and marshmallows are golden brown, about 25 minutes.