Special equipment: 2 disposable piping bags, a 15-by10-inch jelly roll pan, a tea towel, a piping bag fitted with a leaf decorator piping tip (leaf tip #70) and a pastry brush
For the cake decorating paste: In the bowl of an electric mixer, cream together the butter and confectioners' sugar. Add the egg white and beat again until it incorporates into the butter and sugar, about 2 minutes. Sift the flour into the mixing bowl and beat on low speed until just combined. Add the 2 food colors and mix until a consistent orange-red is achieved. Transfer the paste to a disposable piping bag and snip a tiny hole in the end using scissors.
Cut a sheet of parchment paper to fit inside a 15-by-10-inch jelly roll pan. Draw horizontal lines onto the paper using a pencil or pen in 1-inch increments. Flip the paper over so that the side with the drawn lines is touching the pan. You should be able to see the lines through the paper. Pipe lines of the cake decorating paste over the lines. Place the pan in the freezer while the sponge cake batter is prepared.
For the whipped egg whites: In the bowl of an electric mixer, whip the egg whites and granulated sugar together to stiff peaks. Set aside.
For the sponge batter: Preheat the oven to 450 degrees F.
In the bowl of an electric mixer, beat the almond flour, confectioners' sugar, all-purpose flour, whole eggs and egg yolk until combined, stopping to scrape down the sides of the bowl as necessary. Add the orange gel food color and mix until incorporated. With a large rubber spatula, gently fold in the whipped egg whites, being careful to not deflate the batter.
Remove the jelly roll pan from the freezer and pour the sponge batter on top. Smooth the batter gently using an offset spatula.
Bake for 5 to 7 minutes, or until the cake springs back when pressed in the center. Remove from the oven and loosen the edges with a small knife. Turn the cake out onto a parchment sheet and peel away the lined parchment paper on top of the cake.
Sprinkle a tea towel with about 1/4 cup confectioners' sugar. Turn the sponge cake onto the tea towel striped-side down. Roll the cake into the tea towel from a short end. Fold the ends of the towel under and let the cake rest at room temperature while the pumpkin spice ganache is prepared.
For the pumpkin spice ganache: Combine the heavy cream, pumpkin puree, pumpkin pie spice and orange food color in a large microwave-safe bowl. Whisk together until the ingredients are incorporated. Heat in the microwave at 30-second intervals until the mixture is hot and steaming but not boiling (about 1 minute).
Immediately add the white chocolate to the steaming mixture and let stand 1 minute. Stir using a whisk until the chocolate is melted and the mixture is smooth. Cover with plastic wrap and chill until set, about 1 1/2 hours. The mixture can also be poured into a shallow 13-by-9-inch baking dish to speed setting.
For the buttercream: In a medium bowl, beat together the butter and confectioners' sugar with an electric mixer until light and fluffy. Add the vanilla extract and food color. Beat again until a consistent green color is achieved. Transfer half of the buttercream to a piping bag fitted with a leaf decorator piping tip (leaf tip #70). Transfer the other half to a piping bag with a tiny hole snipped in the end.
For the assembly: Carefully unroll the cake and remove it from the tea towel. Allow the tightly curled end of the cake to remain curled. Spread the inside of the cake evenly with the chilled pumpkin spice ganache. Roll the cake up jelly roll style.
Combine the granulated sugar and 1/4 cup water in a small microwave-safe bowl. Heat at 30-second intervals until the sugar is dissolved. Let cool slightly. Gently coat the outside of the cake roll with the sugar syrup using a pastry brush. Use just enough to remove the confectioners' sugar appearance on the cake's exterior. You may not have to use all of the syrup.
Cut the cake evenly into 4 pieces using a serrated knife. Stand each piece upright on a large serving platter (or 4 small plates) so that the stripes are vertical. Break each wafer cookie in half and insert them upright into the centers of the cakes to create pumpkin stems.
Use the piping bag of green buttercream fitted with the leaf tip to pipe leaves next to the wafer stems. Use the other piping bag of buttercream to draw curling pumpkin vines next to the stems and leaves.
Serve immediately to delighted guests.