Add the sweet potatoes to your 6-quart Dutch oven and add water. Cover and cook on the stove over medium heat for 15 to 18 minutes, stirring once, until you can pierce them easily. If any water is left in the pot, drain it off.
Take the pot off the heat. Add the butter, brown sugar, milk, vanilla, cinnamon and salt. Mash until smooth.
Let it sit for 5 minutes to cool slightly, then stir in the beaten eggs.
Smooth the top. Bake uncovered for 30 minutes, until the edges are set and slightly puffed.
Scatter the marshmallows over the top in one snug layer. I like to make it pretty thick, but feel free to use as much as you would like. Increase the temperature to 450°F and bake 5 minutes at most. Keep an eye on them. The tops of the marshmallows burn easily.
Rest for 10 minutes before serving.
Notes
Let the sweet potato mash cool for those 5 minutes before the eggs go in; otherwise they can curdle.
For the marshmallows, lay them in a single snug layer rather than piling them. They puff as they bake and close the gaps on their own.
Watch the marshmallows closely in the oven. They go from golden to burnt in under a minute.