Place the cubed sweet potatoes in a large pot and cover them with water. Bring the water to a boil over high heat, then reduce the heat and simmer for about 15 to 20 minutes until the potatoes are very tender when pierced with a fork. Drain the potatoes well and return them to the pot or a large mixing bowl.
While the potatoes are still warm, add the butter, milk, brown sugar, alcohol-free vanilla, cinnamon, nutmeg, and salt. Use a potato masher or an electric hand mixer to blend everything until the mixture is smooth and creamy. Taste the mixture and add a pinch more salt or spice if you desire a deeper flavor profile.
Once the potato mixture has cooled slightly, whisk in the beaten eggs. Adding the eggs while the potatoes are not boiling hot prevents them from scrambling, and they will help the casserole set with a light, souffle-like texture during the baking process.
Preheat your oven to 350 degrees Fahrenheit. Spread the sweet potato mixture evenly into a greased 9×13 inch baking dish. Place the dish in the oven and bake for 25 to 30 minutes, or until the edges are slightly golden and the center is set.
Remove the dish from the oven and sprinkle the plant-based marshmallows evenly over the top. Return the casserole to the oven for an additional 5 to 10 minutes. Watch closely during this stage, as the marshmallows can go from perfectly golden to burnt very quickly. Once the tops are toasted to your liking, remove the dish and let it rest for a few minutes before serving.
