The sweet potatoes are cleaned and then peeled and cut into eighths. In a large pot, the sweet potatoes are covered with water, brought to a boil, and then the heat is lowered. We simmer the sweet potatoes for 15 minutes until the pieces are tender.
After draining the potatoes in a colander, we allow them to cool for a few minutes. Then, in a large bowl, we combine the sweet potatoes, milk, brown sugar, salt and vanilla. We beat with a whisk until smooth. The eggs are added and the mixture is beat again.
The tablespoon of butter is spread into a 9 inch x 13 inch glass baking pan. Then the sweet potato mixture is poured in. We bake this in the oven for 20 minutes and when it is hot, we add the marshmallows to the casserole, spreading them carefully in one layer. We bake for about 15 minutes until the marshmallows are golden.