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To make the sweet potato purée: Preheat the oven to 400°F with one rack in the middle and one in the upper third. Using a paring knife or fork, pierce the sweet potatoes several times. Place them on a baking sheet lined with parchment or foil and bake for 45 to 60 minutes, until tender. Carefully slice the baked potatoes in half lengthwise and set aside until they're cool enough to handle. Reduce the oven temperature to 350°F.
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Remove the skin from the sweet potatoes and transfer the flesh to the bowl of a food processor. Add the water and process until smooth, about 1 minute. Pause the food processor and scrape the bowl to ensure the mixture is fully combined. Measure 1 3/4 cups (420g) of the purée for use in the recipe and set aside.
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Lightly grease a 9" x 13" pan. Line with a parchment sling and lightly grease the parchment.
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In a medium bowl, whisk together the flour, baking powder, baking soda, spices, and salt. Set aside.
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In a large bowl, place the melted butter. Whisk in the sugar until well combined, then add the sweet potato purée. Whisk until well combined.
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Add the orange juice, egg yolks, vanilla, and food coloring, and whisk until well combined.
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Add the dry ingredients to the wet ingredients in two additions, using a flexible spatula to fold the thick batter together gently after each addition.
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In a small bowl, vigorously whisk the egg whites until foamy; no liquid egg should remain at the bottom of the bowl. Gently fold the beaten egg whites into the batter until well combined and no streaks of egg white are visible.
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Transfer the batter to the prepared pan and spread it into an even layer.
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Bake the sweet potato sheet cake on the middle rack for 35 to 40 minutes, or until a toothpick or thin knife inserted into the center comes out clean and the top feels set. Remove the cake from the oven and let it cool on a rack for about 30 minutes. Use the parchment sling to carefully transfer the cake from the pan to a rack to cool completely.
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To make the marshmallow topping: In a large heatproof mixing bowl or the bowl of a stand mixer, whisk together the sugar, egg whites, vanilla, salt, and cream of tartar or lemon juice until combined.
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Place the bowl over a saucepan of simmering water (you should see just a few small bubbles coming up to the surface) and whisk constantly until the mixture measures 161°F on a digital thermometer, 5 to 10 minutes. The egg whites will be very warm to the touch, and the sugar should be fully dissolved. (Test to see if the sugar is fully dissolved by dipping your fingertip into the mixture and then rubbing your fingertips together; you should not be able to feel any grains of sugar.)
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Remove the bowl from the heat and beat the mixture using the whisk attachment until stiff peaks form, 10 to 13 minutes on medium-high speed.
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To assemble the sweet potato sheet cake: Transfer the marshmallow topping to the top of the cake. Use the back of a spoon or an offset spatula to spread it evenly over the top, creating decorative swirls. Toast the marshmallow topping with a baker's torch or carefully broil the cake in the upper third of the oven until the edges of the topping are golden brown. (If broiling, watch the cake carefully: It can burn quickly!) Sprinkle with toasted nuts and serve.
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Storage information: Store leftover sweet potato sheet cake, covered, at room temperature for up to 3 days.
