Preheat the oven to 350ºF. Grease a three-quart casserole dish with butter. Bring a large pot of water to a boil over high heat. While waiting for the water to boil, peel and dice the sweet potatoes into one-inch cubes.
Add the cubed sweet potato to the boiling water and boil until they are fork-tender. Drain the sweet potatoes then add them to a large bowl and mash them until they are smooth.
Add the brown sugar and salted butter to a medium pan and heat over medium. Whisk the mixture until the butter and sugar melts and a caramel forms.
Add the cream to the caramel and whisk to combine, then add the salt, vanilla, nutmeg, and cinnamon and whisk to combine again.
Mix the caramel into the sweet potato mash. Transfer the sweet potato mash to the greased casserole dish and smooth the top with a spatula.
Top the casserole with 2 cups mini marshmallows (more or less to your liking).*
Bake the sweet potato casserole in the preheated 350ºF oven until the marshmallows are golden, about 20 minutes.