Heat the oven to 350°F. Butter a 1-1½ quart baking dish. Place the sweet potato chunks in a large saucepan and cover them with cool water by about one inch. Bring to a boil, then reduce to a steady simmer.
Simmer the sweet potatoes for approximately 15 to 20 minutes. Drain the potatoes thoroughly. Let the potatoes cool for approximately five minutes. Mash the potatoes until mostly smooth in a mixing bowl. A few very small lumps are acceptable.
Stir in the melted butter, brown sugar, milk, vanilla, pumpkin pie spice and salt. When the mixture is warm rather than steaming hot, stir in the beaten eggs until fully incorporated.
In a medium bowl, combine the pecans, flour, brown sugar, cinnamon, and salt. Stir in the melted butter until the mixture forms moist crumbs. Spread the filling evenly in the buttered baking dish. Sprinkle the pecan mixture evenly across the surface.
Bake uncovered for 20. After 20 minutes, scatter the mini marshmallows over the top. Bake for another 10-15 minutes. Watch closely, remove the casserole when the marshmallows are puffed and lightly golden.
Let the casserole rest for 5 minutes before serving. Eat and enjoy!