Peel and seed squash; cut into 1-inch cubes (you should have 7 to 8 cups). In a large bowl, mix squash with sugar. Let stand until sugar liquefies, about 30 minutes. Stir, then pour into a deep 2 1/2- to 3-quart baking dish. Crumple a piece of baking parchment larger than the dish opening, moisten with water, then flatten it and cover squash, tucking paper around inside of dish.
Bake in a 300° oven (see notes) until squash is tender when pierced, 1 1/2 to 2 hours. Turn off oven and leave squash inside until completely cool, about 3 hours.
Shortly before serving, in a 6- to 8-inch frying pan over medium heat, stir walnuts and butter until nuts are coated with butter and lightly browned, about 3 minutes. Spoon squash and syrup into small bowls. Garnish each serving with a generous dollop of crème fraîche and a sprinkle of walnuts.