Preheat oven to 350 degrees
In a large pot, bring about 6-8 cups of water to a boil and add the sweet potatoes -allow it cook for 35-50 minutes or until tender
Remove from heat and drain water out of pot
Mash the sweet potatoes
Add the butter , brown sugar and white sugar then mix well
Add cinnamon , nutmeg , half and half , beaten eggs, rum, and vanilla extract and mix well
Pour the mixture into a casserole dish that had been sprayed with non stick spray
Sprinkle the top with the mini marshmallows
Lightly sprinkle cinnamon over the marshmallows
Place in the oven and bake for about 1 hour
Remove from heat , allow it to cool for 5-10 minutes, and serve !