Preheat the oven to 350 degrees F and grease a 9-by-13-inch baking dish.
Soak the stale bread in the milk in a large bowl for 20 minutes.
Heat the oil in a large skillet over medium-high heat. Add the shallots, onions, carrots and celery and cook 10 minutes until wilted.
Drain the milk from the bread by pressing with your hands. Add the bread to a large bowl, then add the sauteed vegetables, egg, sage, parsley, grated orange rind and 1/2 cup of the grated cheese. Season with salt and pepper and mix until all the ingredients are incorporated and the stuffing is well blended. Add the chestnuts and mix well.
Spoon into the prepared baking dish and shake into place with a rubber spatula. Cover with aluminum foil and bake for 30 minutes. Uncover, sprinkle on the remaining 1/2 cup grated cheese and cook an additional 20 minutes or until crispy on top.