Preheat your oven to 350°F. Spray a 2-quart casserole dish with non-stick spray and set aside.Peel and dice the sweet potatoes. Place them in a large stock pot, cover with water, and bring to a boil. Cook for about 15 minutes, or until tender. Strain the sweet potatoes and transfer them to the bowl of a stand mixer. Mix on low for about 2 minutes until mashed, scraping down the sides often.
While the potatoes are still warm, add the butter and mix well.
Add milk, brown sugar, egg, vanilla, cinnamon, allspice, salt, and nutmeg. Mix thoroughly, scraping down the sides as needed.
Transfer the sweet potato mixture to the prepared casserole dish and bake for 40 minutes.
Remove from the oven and sprinkle the mini marshmallows over the top, spreading them into an even layer.
Bake for an additional 5 minutes, or until the marshmallows are slightly toasted and starting to melt.
Let the casserole cool slightly before serving.