Combine the brown sugar, sugar, cinnamon, nutmeg and salt in a small bowl and set aside.
In a large skillet or Dutch oven, melt the butter over medium heat. Add the sliced sweet potatoes and toss to coat with butter. Sprinkle the sugar mixture over the buttered potatoes and stir to coat. Reduce heat to low, cover skillet, and continue cooking for one hour; stirring occasionally. Once the sauce has caramelized the potatoes and they’re fork-tender, stir in the vanilla. The sauce will thicken slightly once off the heat.