Preheat oven to 400 degrees. Line a rimmed baking sheet with parchment paper. Place sweet potato on sheet, and cover with foil. Bake 20 minutes. Add apple. Cover; bake until tender, about 20 minutes. Remove from oven; uncover, and transfer to a wire rack. Let cool completely, about 15 minutes. Leave oven on.
Transfer sweet potato and apple to a food processor. Add salt, allspice, and 1 tablespoon granulated sugar; puree. Pulse in 1 to 2 tablespoons water, if needed, to achieve a smooth consistency. Pass through a medium sieve into a medium bowl. Stir in egg yolk and flour; set aside.
Put egg whites in the bowl of an electric mixer fitted with the whisk attachment. Beat on medium-high speed until soft peaks form. Gradually add remaining 2 tablespoons granulated sugar, beating until stiff, glossy peaks form. (Do not overbeat.) Whisk one-third of the egg white mixture into the sweet potato mixture. Using a rubber spatula, gently fold in remaining egg white mixture.
Divide among six 6-ounce ramekins. Place on a rimmed baking sheet. Bake until puffed and cooked through, about 14 minutes. Sprinkle with confectioners' sugar, and serve immediately.