Preheat oven to 375 degrees F and butter a baking dish.
In a food processor, puree the carrots, onion, celery and sage until you have a fine pulp. Set aside.
Place in a large skillet over medium-high heat and brown the sausage and garlic in 1 tablespoon of olive oil, about 5 minutes. Remove the sausage and garlic from the pan and place on a plate lined with a paper towel to absorb the oil.
Add the vegetable pulp to the pan and saute until most of the moisture has evaporated. Place the sausage, vegetable pulp, bread cubes and chestnuts in a large mixing bowl.
Season with salt and pepper.
In another bowl mix together the chicken broth, cream and egg. Pour this wet mixture over the dressing mix.
Fold everything together. Pour out into baking dish and bake for 30 to 35 minutes until golden brown on top.