Preheat oven to 375 degrees F. Grease a jellyroll pan, line with waxed paper, and grease the paper.
Combine apples, cranberry sauce, sugar, water, apple juice, lemon juice, cinnamon, and nutmeg in a non-reactive heavy-bottomed saucepan. Cook over medium heat, stirring until mixture thickens, about 6 minutes. Set aside to cool.
For cake, sift together flour, baking powder, and salt on a piece of waxed paper, set aside. Beat eggs in medium bowl for 2 minutes. Gradually beat in sugar until thick and pale, about 5 minutes. Stir in water and vanilla. Fold in flour mixture and ground walnuts.
Pour into the prepared pan spreading evenly. Bake for 12 minutes.
Loosen cake around the edges with a knife. Invert the pan onto a clean towel dusted with powdered sugar. Remove from the pan. Carefully peel away waxed paper. Starting at short end, roll cake and towel together. Cool on a wire rack about 30 minutes.
When cake is cool, unroll carefully. Spread roll evenly with prepared fruit filling, leaving a 2-inch border along the short side, which will be the outside seam. Reroll the cake from short end, using towel as an aid. Place roll, seam side down, on serving platter.
Whip together frosting ingredients. Place into a pastry bag fitted with a star tip. Pipe whipped frosting around edges and on top of cake roll.
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.