Heat the oven to 375°F. Melt butter in a skillet and cook onion and celery for 5 minutes until softened. Stir in broth, sage and 1/4 teaspoon salt, bring to a simmer and fold into the bread cubes.
Cut a deep pocket into the side of each chop with a small knife, keeping the other edges intact. Spoon warm stuffing loosely into the pockets and secure the openings with wooden toothpicks; season the pork with remaining salt and pepper.
Heat oil in a large oven-safe skillet and brown chops for 2 minutes per side, working in two batches if needed. Return all chops to the skillet in one layer or transfer to a baking dish.
Bake for 20 to 30 minutes until the center of the stuffing reaches 165°F and the pork itself is at least 145°F. Check both locations in the thickest chop.
Rest for at least 3 minutes, remove every toothpick and serve with any hot pan juices spooned beside the chops.