Spray a 15 by 10 by 1-inch baking sheet with vegetable oil spray. Line the pan with parchment paper and butter the top of paper. Place nuts, both sugars, ginger slices, almond extract, and cake flour into food processor. Process until nuts are finely ground.
Beat the egg whites in a large, clean bowl until stiff, forming peaks, but not dry. Fold nut mixture into beaten egg whites in 3 separate additions (the egg whites will collapse if too much nut mixture is added all at once). Add cake mixture to prepared pan and spread evenly. Bake for 30 minutes or until cake is lightly golden on top. The cake will be moist. Do not overbake. Cool cake for 10 minutes in the pan. Turn out onto cooling rack and cool until cake is slightly warm.
To Assemble Cake:
Line a 2 1/2 quart bowl with plastic wrap overlapping sides by 3 inches. Cut cake lengthwise into 1/3-inch wide strips. Line bowl with cake strips placing slices tightly side by side with cut side down in a single layer, trimming to fit and completely covering bowl. If cake slices break, piece together to fit. Brush cake with 2 tablespoons amaretto. Spread ganache over cake covering completely. Gently press peanut butter chips into ganache. Spread peanut cream into center and smooth top. Cover filling with remaining cake, placing slices side by side, fitting tightly together and trimming to fit. Brush with remaining 1 tablespoon amaretto. Fold excess plastic wrap over top. If plastic wrap does not cover cake completely, cover with more wrap. Chill at least 4 hours or overnight.
Garnish the cake with Apricot Roses and the Sugar Cage.
Heat the heavy cream, butter and sugar in a 2 1/2 quart saucepan over medium high heat. When hot, stir to dissolve the sugar. Bring the mixture to a boil. Place the chocolate in a stainless steel bowl. Pour the boiling cream over the chocolate and allow to stand for 5 minutes. Stir until smooth. Allow the ganache to cool to room temperature.
Add chilled whipping cream and stabilizer to a large bowl. Beat until soft peaks form. Gradually add sugar and beat until cream is firm. Fold amaretto into whipped cream in 2 additions. Add chopped nuts, chocolate and zest into a bowl and stir to combine. Gently fold nut mixture into soft whipped cream in 2 additions trying not to deflate whipped cream.
Roll each apricot out, sticky side down, between 2 sheets of waxed paper to 1/16-inch thickness. Roll up tightly, sticky side in, to form a tight center bud of a rose. Wrap another apricot around the bud, sticky side in, pressing gently to stick together. Repeat with 2 more apricots, overlapping half of each previous wrap. Gently bend top of outer 3 apricots outward to form petals. Place toothpicks through bottom of rose and cut off apricot below toothpick to form a flat base. Repeat until desired number of roses are complete. Place roses on a plate and freeze for 30 minutes. Garnish finished cake with apricots roses.
Place sugar, corn syrup, and water in a heavy 2-quart saucepan over medium high heat. Cook the sugar mixture until it reaches the hard-crack stage (310 to 320 degrees F). Remove the pan from heat and carefully pour into a heatproof microwaveable glass bowl. Do not leave sugar in the pan because it will continue to cook and turn brown. (If sugar thickens and is not easy to work with, place the sugar into the microwave for 3 to 5 minutes to thin.)
Spray a bowl (large enough to fit over cake) lightly with vegetable oil. Dip a fork into the hot sugar and quickly wave the fork over the inside of the bowl in a swirling motion allowing the sugar to drip off the fork in long, thin strands distributing evenly on the sides and bottom of the bowl making sure the sugar comes up to the rim. Set aside to cool about 5 minutes. Gently pull the "cage" loose from the side and bottom of the bowl. If the sugar is too warm, the cage may collapse. Place cage over finished cake.
Be extremely careful when working with cooked sugar. The temperature of the sugar exceeds the temperature of boiling water and can be very dangerous.
A viewer or guest of the show, who may not be a professional cook, provided this recipe. It has not been tested for home use.