Pierce potatoes a few times with a fork. Roast in a 400°F oven until tender, about 50 min. Let cool enough to handle, then peel and dice. Toss with salt and brown sugar and arrange in a 2-qt baking dish. Bake, covered, until heated through, about 25 min.
While potatoes are heating, make meringue: In the bowl of an electric mixer combine egg whites, sugar and cream of tartar; set bowl over a pan of simmering water. Whisk until sugar is dissolved and mixture is hot, about 3 min.
Transfer to mixer and whip on high until stiff peaks form, about 7 min. Stir in cinnamon.
Heat broiler to high or prepare a kitchen torch. Spoon meringue over potatoes and toast under the broiler or with a kitchen torch.
You can place the finished dish under the broiler to get a toasty top on the meringue, or flash it with a cooking torch. I use one like this. The toasted top tastes just like mom's crispy-topped marshmallows. So good!