Spiced Sweet-Potato Cake with Meringue Frosting

For the Cake: Preheat oven to 375°F. Prick sweet potatoes with a fork and place on a rimmed baking sheet. Roast until soft, about 1 hour, 15 minutes. Halve, scoop flesh from skins, and mash until smooth (you should have about 1 1/4 cups). Let cool, then refrigerate in an airtight container up to 3 days.

Lower oven temperature to 350°F. Brush a 9-by-13-inch cake pan or baking dish with butter. Line bottom and two long sides with parchment, leaving a slight overhang on sides; brush parchment with butter.

In a bowl, whisk together both flours, baking powder, baking soda, salt, and spices until aerated and thoroughly combined, 30 seconds. In a mixer, beat butter with brown sugar on medium-high speed until pale and fluffy, 2 to 3 minutes. Beat in eggs, one at a time, then vanilla and potato mash to thoroughly combine (mixture will appear grainy). Reduce speed to low and beat in flour mixture in three additions, alternating with buttermilk and beginning and ending with flour mixture. Transfer batter to prepared pan and spread evenly to edges with an offset spatula.

Bake until cake is set and springs back when lightly pressed in center, about 30 minutes. Let cool in pan 10 minutes. Flip out onto a wire rack, remove parchment, and let cool completely.

For the Frosting: In a small saucepan, bring granulated sugar, 1/4 cup water, and corn syrup to a boil, stirring until sugar has dissolved. Cook, undisturbed, until syrup registers 248°F on a candy thermometer. Meanwhile, in a mixer fitted with the whisk attachment, beat egg whites on medium-low speed until foamy. Add salt and cream of tartar, increase speed to medium, and beat until soft peaks form, 3 to 4 minutes. Reduce speed to medium-low and pour hot syrup down the side of the bowl in a slow, steady stream. Increase speed to high; beat until mixture cools slightly and reaches stiff, glossy peaks, about 3 minutes.

Transfer frosting to a piping bag fitted with a large, plain round tip (or transfer to a resealable freezer bag and snip off one corner). Starting at one corner of cake, pipe frosting lengthwise to form side-by-side rows. Wave a kitchen torch over frosting to brown in places (or place frosted cake under broiler for 1 to 2 minutes).