Place the sweet potatoes in a pot and cover them with water. Cover the pot and bring to a boil. Reduce heat to medium, and simmer until very tender. Allow the sweet potatoes to cool for 15-20 minutes, or until you can handle them.
Cut them in half and scoop the inside of sweet potatoes out with a spoon (discard the skin). Place the sweet potatoes, vanilla extract, cinnamon and nutmeg in a food processor. Process until smooth, adding the condensed milk until desired consistency (pudding-like texture) is achieved.
Spoon the sweet potato pudding into a serving bowl or individual dishes. Garnish with walnuts and refrigerate for at least 6-7 hours or overnight before serving.