Preheat oven to 400 degrees.
Toast bread in 1 tbsp. butter in an oven-proof skillet over medium-high heat until crisp and then transfer to a bowl. Return pan to heat.
Saute onion, celery, and apples in 1 tablespoon butter over medium heat until soft. Stir in thyme. Add vegetables to bread cubes. Toss the mixture with the chicken broth, vinegar, and seasonings until the liquid is absorbed. Wipe out the skillet.
Prepare chops by cutting a pocket at the midway point of each chop being careful only to cut through on one side.
Fill pockets with bread mixture. They will be full, but you’ll probably have some left-over stuffing.
Saute chops in oil over medium-high heat until brown on one side, about 3 minutes. Carefully turn the chops over and add any extra stuffing to the pan at this point.
Transfer pan to the oven. Roast about 8 minutes, then remove the chops and stuffing from the pan and set aside. Tent with foil to keep warm.
Saute shallots for the sauce in 1 tablespoon of butter in the same skillet over medium heat. Add flour and cook for 1 minute.
Deglaze the pan with cider, wine, and vinegar. Simmer until sauce is slightly thickened, about 2-3 minutes. Finish sauce with thyme, salt, and pepper.
