Heat the unsalted butter and extra-virgin olive oil in a large skillet over medium-high heat until the butter is melted and bubbling. Add the diced onion, chopped celery, and minced garlic. Cook, stirring often, until the vegetables are softened and the onion becomes translucent, about 3 to 4 minutes.
Add the peeled and diced apples to the skillet along with the chopped fresh sage, chopped fresh thyme, salt, coarse ground black pepper, and ground cinnamon. Continue to cook, stirring, for 1 to 2 minutes until the apples begin to soften and the herbs are fragrant and well combined with the vegetables.
Pour in the apple cider and stir well, allowing the mixture to simmer until the cider is mostly evaporated, about 2 to 3 minutes. Add the chicken broth (or alternative stock) to the skillet and bring everything to a simmer. This will infuse the vegetables and aromatics with savory and sweet notes.
In a large bowl, whisk the eggs thoroughly. Carefully ladle about 1 cup of the hot apple, vegetable, and broth mixture into the eggs while whisking constantly to temper them and prevent scrambling. Gradually stir in the remaining hot vegetable and broth mixture, mixing well to fully incorporate. I always temper the eggs gently so the final stuffing has a rich but smooth custard texture.
Add the cornbread stuffing cubes and the toasted chopped pecans to the bowl with the egg and vegetable mixture. Toss everything together until the stuffing is evenly moistened and combined. Lightly coat a 9x13-inch (or similar) baking dish with cooking spray or a bit of butter. Transfer the stuffing mixture into the prepared dish and cover with foil. At this point, you can refrigerate the stuffing for up to 24 hours if desired.
Preheat the oven to 350°F (175°C). Bake the covered stuffing dish (with foil) until heated through—35 to 45 minutes if starting from refrigerated, or 25 to 30 minutes if freshly mixed. Remove the foil and bake for another 10 to 15 minutes, or until the top is beautifully browned and slightly crisp. I like to let my stuffing rest for 10 minutes after baking so the flavors settle and it slices neatly.