Preheat the oven to 375 degrees F and butter a 9 by 11-inch baking dish.
In a food processor puree the carrot, onion, celery and sage until you have a fine pulp. Set a large skillet over medium-high heat and brown the sausage in a little olive oil. Once you have a nice brown color and the fat has rendered - about 5 minutes, use a slotted spoon to remove the sausage and place in a large mixing bowl. Add the vegetable pulp to the pan and saute until most of the moisture has evaporated. Season with salt and pepper. Add to the mixing bowl with the sausage and also add the bread crumbs and chestnuts.
Mix together chicken stock, cream and egg. Pour this wet mixture over the dressing mix. Season and fold everything together. Pour out into the roasting dish and bake for 30 to 35 minutes until golden brown on the top (if it gets too brown before the 30 minutes is up, tent with foil).