Peel the sweet potatoes, chop them finely and boil until softened with the lid closed. Mash them.
Mix the eggs with the sugar and milk. Heat them in a water bath until thickened.
Cool and mix them with the potato puree. Beat the cream with the rum and add it to the potato mixture.
Put it in a suitable plastic or metal container and freeze for 6 hours in the freezer, stirring every 2 hours.