Lightly scrub the sweet potatoes under cold running water. Place the potatoes on a roasting tray and bake until tender, 1 hour 15 minutes. Remove from the oven and allow the potatoes to cool slightly before cutting off the top third of the potatoes lengthwise. Scoop out the flesh using a large spoon (leave enough on the base so the skin holds its shape) and reserve bases.
Add the potato flesh, 2 tablespoons of the sugar, cinnamon, nutmeg, cayenne pepper and butter to a food processor. Process until the ingredients are completely combined and the puree is smooth. Season with salt and pepper. Drizzle a roasting tray with a little oil. Set the potato skin bases upright on the tray and fill with the mixture.
Combine the remaining 3 tablespoons sugar and pecans in a small bowl. Sprinkle the top of each stuffed sweet potato with the sugar-pecan topping. Bake 10 minutes. Finish the potatoes under the broiler for the top to brown, 1 minute, if desired.