Heat oven to 325 degrees Fahrenheit. Line a jelly roll pan (10 x 15 inches) with parchment paper so that the two long edges are hanging over (so that you can easily lift the cake out after baking). Set aside.

In the bowl of a stand mixer fitted with a beater attachment, beat eggs and sugar on medium until combined. Add vanilla extract, pumpkin puree, and salt and again beat on medium until incorporated. Add baking powder and flour and beat just until combined. Turn batter out onto the prepared jelly roll pan and use a spatula to spread in a thin, even layer to the edges. Bake in heated oven for 20 minutes, until a finger leaves no indentation in the cake.

Remove from oven and allow to cool for just a few minutes. Using the parchment paper tabs, carefully lift the cake out of the jelly roll pan and place on a kitchen towel. Starting at one of the short edges (without the parchment paper overhang), gently and carefully roll up the cake and parchment into the towel into a log shape. Place on a wire rack to cool to room temperature before filling.

Place hazelnuts in a kitchen towel on top of a wooden cutting board. Gently hammer with either a meat mallet or the bottom of a saucepan until crushed. I prefer to have some smaller pieces and some larger pieces, but crush until whatever texture you prefer!

In the bowl of a double boiler set over simmering water, combine white chocolate and 1/4 cup of the whipping cream. Allow to melt, stirring occasionally, until the mixture is smooth and homogenous. Remove from stove and allow mixture to cool for 10 minutes.

In the bowl of a stand mixer fitted with a whisk attachment, beat remaining 1 cup of chilled whipping cream until soft peaks form. Add white chocolate mixture and whisk until combined.

When the cake is cooled completely to room temperature, unroll the log carefully and remove parchment paper and kitchen towel. Spread the white chocolate mousse over the whole log, leaving a 1/2 inch border at the edges. Sprinkle with the crushed hazelnuts. Re-roll the log up (without parchment paper or towel) and wrap tightly in plastic wrap or tinfoil. Chill in the refrigerator for at least one hour before serving, to make slicing easier. If you prefer a prettier edge, cut a small sliver off each end to give a clean edge. Dust with powdered sugar before serving!