Cook the chestnuts in butter over medium heat for about 10 minutes stirring constantly until browned. Remove pan from fire, add brandy and return to burner to flame the brandy. Add chicken stock and cook until glazed. Reserve.
Saute onion and garlic in oil for 5 minutes to soften. Add button mushrooms and white wine. Reduce the liquid, add water and thyme. Cook 10 minutes on low heat. Pour all ingredients into a blender and puree, strain and season with salt and pepper. Return to a medium heat and whisk in creme fraiche.
Bring a large pot of boiling, salted water to a boil. Add the pasta sheets and cook until al dente, about 4 minutes.
In a small saute pan, heat some olive oil. When the oil is hot, add the sage leaves and fry until crispy, about 30 seconds. Remove and drain on paper towels.
Place 1 large spoon full of butternut squash puree on a plate. Place 1 pasta sheet on top of the puree and push down. Place 1 large spoonful of acorn squash puree on the pasta sheet and top with one more pasta sheet. Spoon some sauce around and place 4 chestnuts in the sauce. Grate some amaretti cookie over the pasta top with fried sage leaf.
Preheat the oven to 350 degrees F.
Place all spices and water in a pan. Put squash flat side down on a wire rack or steaming basket above water. Cover with foil and bake 1 hour, until tender. Remove meat and puree with the mascarpone in food processor. Season with salt and pepper.
Preheat the oven to 400 degrees F.
Cut squash in 1/4's. Drizzle with olive oil, salt and pepper. Place on flat sheet tray. Roast until tender, about 35 minutes. Remove meat from squash. Heat a saute pan over medium heat. Add the butter and cook until the butter has browned and smells nutty, about 5 minutes. Puree squash, butter, sage leaves, garlic and salt and pepper, to taste, in food processor.