Using a hand blender, in a large bowl, add egg yolks and white sugar, mix until pale yellow and thick, add brown sugar, mascarpone and beat, until combined. Then add butternut squash puree, blend well.
Using a spatula, add whipped cream, and fold gently into egg mixture.
Beat Egg Whites to soft peaks, fold the egg whites into mascarpone cream
In a large bowl, add espresso coffee and vanilla extract. Mix well.
Dip ladyfingers in coffee one at a time and place in a large baking dish forming a layer, cover bottom dish.
Place butternut squash mascarpone filling on top and spread over cookies. Repeat for each layer, finishing top with cream filling.
Dust top with cocoa powder and cover with saran wrap and place in fridge for 2 to 24 hours, until ready to serve.