Step 1

In a 9- by 13-inch baking dish, arrange sweet potato rounds in an even layer, overlapping where necessary to fit them all. Set aside.

Step 2

In a small saucepan, combine brown sugar, butter, water, and salt and bring to a boil, stirring often, until syrup registers 220°F (104°C) on an instant-read thermometer. Stir in cider vinegar, cinnamon, allspice, and ginger, then pour syrup all over potatoes, spooning it over them as necessary to wet them completely.

Step 3

Cover baking dish with aluminum foil and place in a cold oven. Turn on oven to 250°F (120°C) and allow it to come up to temperature. Cook, stopping to flip and baste potatoes with syrup every 20 minutes, until tender throughout, about 1 hour 15 minutes. (Exact cooking time will depend on your oven, baking dish, and the size of your potatoes, so check frequently.)

Step 4

Remove foil and continue to cook, flipping and basting potatoes occasionally, until they are very soft and glazed in a rich brown syrup, about 30 minutes longer. Let cool slightly, then serve.