Preheat the oven to 400 degrees F.
Wash the sweet potatoes, halve them lengthwise and then cut each half again similarly into 3 long wedges. Mix with 3 tablespoons of the olive oil, 2 teaspoons salt and some black pepper. Spread the wedges out, skins die down, on a baking sheet and cook for bout 25 minutes, until soft but not musty. Remove from the oven and leave to cool down.
To make the balsamic reduction, place the balsamic vinegar and sugar in a small saucepan. Bring to a boil, then decrease the heat and simmer for 2 to 4 minutes, until it thickens. Be sure to remove the pan from the heat when the vinegar is still runnier than honey, it will continue to thicken as it cools. Stir in a drop of water before serving it it does become too thick to drizzle.
Arrange the sweet potatoes in a big salad dish. Heat a tablespoon of olive oil in medium saucepan over medium heat and add the green onions and chile. Fry for 4 to 5 minutes, stirring often to make sure not to burn the chile. Spoon the oil, onions and chile over the sweet potatoes. Dot the figs amount the wedges, crumble the cheese over the top and then drizzle over the balsamic reduction. Serve at room temperature.