With a small paring knife, cut an x in the center of each chestnut. Rub the chestnuts lightly with vegetable oil. Place the oiled chestnuts on flat sheet pan and bake in the preheated oven for 7 to 8 minutes or until they pop. Let the chestnuts sit until cool enough to handle. Peel them and chop them into medium pieces. Reserve.

Coat a large heavy stockpot set over medium heat with 2 tablespoons vegetable oil. When the oil is hot, add the chopped onion, celery, carrot and cabbage. Let the vegetables cook for approximately 5 minutes until they soften. Season with sea salt. Add enough water to cover the vegetables by one inch. Bring the mixture to a low boil. Reduce the heat and let the stock simmer for 35 minutes. Strain and discard vegetables.

Peel and chop the squash in 1/2 inch pieces. In a heavy stockpot over low heat, melt the butter. Add the diced squash. Let cook until the squash is soft. Add the allspice and enough vegetable stock to cover the squash by one inch. simmer for 10 minutes.

Let the soup cool briefly. Puree in a blender. Add the carrot juice and half and half. Season with salt and pepper. Reheat gently.