Heat a large cast iron skillet (or other heavy oven-safe skillet) over medium heat. Once hot, add 1 tablespoon of the oil. When oil starts to shimmer, add the andouille and brown for 2 minutes, breaking it up into smaller pieces. Add the onion, celery, and carrots, and then stir well and cook for 2 more minutes. Stir in the garlic and cook until onion is translucent and softened.

Transfer andouille mixture to a medium bowl and then add the pecans, bread crumbs, thyme, parsley, cayenne, salt, and pepper. Mix well.

Preheat oven to 350° F.

With a sharp knife, cut a deep wide pocket into each pork chop. Divide the stuffing evenly between the 4 chops and pack it into each pocket. Sprinkle both sides of chops with a little kosher salt and freshly ground black pepper.

Heat the same cast iron skillet again over medium high heat. Add the remaining 2 tablespoons of oil. When the oil is hot and shimmering, add the chops. Sauté until nicely browned, about 4 minutes per side.

Immediately transfer the whole skillet with the pork chops to the oven. Bake for about 7 minutes, or until internal pork chop temperature is 140° F. Pull the skillet out of the oven and let rest on the stove top for a bit, until the temperature rises to 145° F. Then serve while still hot.