Place sweet potatoes into a large pot and cover with salted water; bring to a boil. Reduce heat to medium-low and simmer until tender, about 20 minutes. Drain. Peel sweet potatoes once they are cool enough to handle. Slice sweet potatoes into 1-inch thick rounds; arrange in a 9x13-inch casserole dish.
Mix brown sugar, butter, maple syrup, vanilla extract, and salt together in a saucepan; bring to a boil, stirring often, until sugar has dissolved and butter has melted, 5 to 10 minutes. Pour sauce over sliced sweet potatoes.
Bake in the preheated oven until heated through and sauce has slightly reduced, about 1 hour. Serve hot.