Preheat oven to 325 degrees F. Cut cornbread and country-style bread into 1/2 to 3/4-inch cubes. You should have about six cups of each. Spread in an even layer on two baking sheets and bake until lightly toasted and dry throughout, about 20 minutes. Set aside to cool.
Raise oven temperature to 375 degrees F. Butter a 3-quart gratin pan and set aside. Place sausage in a medium skillet over medium-high heat and cook, breaking sausage up with a wooden spatula or spoon, until cooked through. Remove from pan and transfer to a large bowl. Add olive oil to pan and sauté chopped celery and onion until softened, about 5-8 minutes. Season with 1/2-teaspoon kosher salt and 1/4 teaspoon pepper.
Add sautéed celery and onion, herbs, and chestnuts to sausage. Stir to combine. Add toasted bread cubes, chicken stock, and apple cider, folding gently to combine. Season to taste with salt and pepper. Gently fold in beaten eggs.
Transfer stuffing mixture to prepared gratin pan. Bake, covered with foil for 30 minutes. Uncover and continue baking 20-25 minutes, until stuffing registers 165 degrees F in the center and is lightly browned and crisp on top.
To make single-serve "Stuffing Muffins"
Butter standard muffin tins (you'll need about 15 wells), including bottoms, sides, and top rims. Use an ice cream scoop to generously mound stuffing into each well, pressing gently to compact. Bake uncovered for 20-25 minutes, until centers reach 165 degrees F and stuffing is crisp on the top. Remove from oven and run a butter knife around the sides of each cup to loosen. Let stand 5 minutes and use a fork to help ease muffins out of wells and onto a serving platter.
*Either your favorite homemade or store-bought cornbread is fine to use here. The loaves I use generally weigh about a pound and are baked in an 8-inch pan.**I love to roast chestnuts at home (such a wonderful aroma!) but almost always use imported jarred chestnuts (such as Clement Faugier or Minerve) when I'm not going to enjoy them on their own and am mixing them into recipes such as stuffing. Convenient and delicious.The amount of salt and pepper needed to season this recipe will depend not only on your personal tastes, but on the saltiness of your stock and amount of spice in your store's brand of Italian sausage. For safety purposes, finish seasoning before raw eggs are added and avoid re-tasting until the stuffing is fully cooked.Since every oven is different, you'll want to keep an eye on the stuffing after it's uncovered to make sure it's not drying out or becoming too crisp. If it looks like it's becoming dry before it reaches the proper internal temperature, just pour a few additional tablespoons of reserved stock over the top to lightly moisten.